What ratio is equivalent to 2 to 17

Answer:

Null hypothesis: [tex]\mu_1 \geq \mu_2[/tex]

Alternative hypothesis: [tex]\mu_1 <\mu_2[/tex]

[tex]t=-1.329[/tex]

[tex]p_v =P(t_{30}<-1.329) =0.0969[/tex]

With the p value obtained and using the significance level given [tex]\alpha=0.1[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 10% of significance the mena of the group 1 is significantly lower than the mean for the group 2.  

Step-by-step explanation:

When we have two independnet samples from two normal distributions with equal variances we are assuming that

[tex]\sigma^2_1 =\sigma^2_2 =\sigma^2[/tex]

And the statistic is given by this formula:

[tex]t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}}+\frac{1}{n_2}}[/tex]

Where t follows a t distribution with [tex]n_1+n_2 -2[/tex] degrees of freedom and the pooled variance [tex]S^2_p[/tex] is given by this formula:

[tex]\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}[/tex]

This last one is an unbiased estimator of the common variance [tex]\simga^2[/tex]

The system of hypothesis on this case are:

Null hypothesis: [tex]\mu_1 \geq \mu_2[/tex]

Alternative hypothesis: [tex]\mu_1 <\mu_2[/tex]

Or equivalently:

Null hypothesis: [tex]\mu_1 - \mu_2 \geq 0[/tex]

Alternative hypothesis: [tex]\mu_1 -\mu_2<0[/tex]

Our notation on this case :

[tex]n_1 =14[/tex] represent the sample size for group 1

[tex]n_2 =18[/tex] represent the sample size for group 2

[tex]\bar X_1 =565[/tex] represent the sample mean for the group 1

[tex]\bar X_2 =578[/tex] represent the sample mean for the group 2

[tex]s_1=28.9[/tex] represent the sample standard deviation for group 1

[tex]s_2=26.3[/tex] represent the sample standard deviation for group 2

First we can begin finding the pooled variance:

[tex]\S^2_p =\frac{(14-1)(28.9)^2 +(18 -1)(26.3)^2}{14 +18 -2}=753.882[/tex]

And the deviation would be just the square root of the variance:

[tex]S_p=27.457[/tex]

And now we can calculate the statistic:

[tex]t=\frac{(565 -578)-(0)}{27.457\sqrt{\frac{1}{14}}+\frac{1}{18}}=-1.329[/tex]

Now we can calculate the degrees of freedom given by:

[tex]df=14+18-2=30[/tex]

And now we can calculate the p value using the altenative hypothesis:

[tex]p_v =P(t_{30}<-1.329) =0.0969[/tex]

So with the p value obtained and using the significance level given [tex]\alpha=0.1[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 10% of significance the mena of the group 1 is significantly lower than the mean for the group 2.  

Answer:

114

Step-by-step explanation:

Given that two intervals  are confidence intervals for μ = mean resonance frequency (in hertz) for all tennis rackets of a certain type.

They are

i) [tex](113.4, 114.6)[/tex] and

ii) [tex](113.1, 114.9)[/tex]

We know that confidence interval has centre as the mean value

Hence we find the average of lower and upper bounds to find out the sample mean.

Sample mean in i) [tex]\frac{113.4+114.6}{2} =114[/tex]

Sample mean in ii) [tex]\frac{113.1+114.9}{2} =114[/tex]

Thus we find that value of sample mean =114

The value of the sample mean resonance frequency is 114 hertz.

The value of the sample mean (in hertz) resonance frequency can be found by taking the average of the lower and upper bounds of the confidence intervals. For the first interval (113.4, 114.6), the sample mean is (113.4 + 114.6) / 2 = 114 hertz. For the second interval (113.1, 114.9), the sample mean is (113.1 + 114.9) / 2 = 114 hertz. So the value of the sample mean resonance frequency is 114 hertz.

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Final answer:

To find the equation of the regression line, calculate the slope and y-intercept using the given formulas with the given data points.

Explanation:

To find the equation of the regression line, we need to calculate the slope and the y-intercept. The slope, b, can be found using the formula:

b = (nΣ(xy) - ΣxΣy) / (nΣ(x^2) - (Σx)^2)

where n is the number of data points, Σ represents summation, x and y are the given data points. The y-intercept, a, can be calculated using the formula:

a = (Σy - bΣx) / n

Substituting the values from the given data into these formulas will give you the equation of the regression line.

Answer:[tex]\frac{1}{\mu }+\frac{1}{\lambda }[/tex]

Step-by-step explanation:

If a machine is replaced at some time t, then the expected time until next failure is [tex]\frac{1}{\mu }[/tex]

and the time between the checks is exponentially distributed with rate \lambda, the expected time until next failure is [tex]\frac{1}{\lambda }[/tex]  

Because of memory less property of the exponential  The answer is

[tex]\frac{1}{\mu }+\frac{1}{\lambda }[/tex]

Answer:

Step-by-step explanation:

the record for the 100 m dash is 12.45 seconds. Since the length of times in the table is relative to the record time, 12.45 seconds,

Pablo's time - 12.45 = -0.12

Pablo's time = -0.12 + 12.45 = 12.33 seconds.

Cindy's time - 12.45 = 0.34

Cindy's time = 0.34 + 12.45 = 12.79 seconds

Eddie's time - 12.45 = -0.15

Eddie's time = -0.15 + 12.45 = 12.3 seconds.

Sam's time - 12.45 = 0.21

Sam's time = 0.21 + 12.45 = 12.66 seconds.

The following statements are true

A. Pablo and Eddie both broke the school record this year.

C. Sam ran the 100-m dash faster than Cindy.

D. Eddie was the fastest runner in the race.

Answer:

A. Pablo and Eddie both broke the school record this year.

Step-by-step explanation:

Current record is 12.45seconds  

Pablo record is -0.12 seconds which is 12.45 – 0.12 = 12.33 seconds  

Eddie’s record is -0.15 seconds which is 12.45 – 0.15 = 12.30 seconds.  

Answer:

Please see attachment

Step-by-step explanation:

Final answer:

To construct the 95% confidence interval for the average time spent in a particular job at General Motors, we calculated the margin of error and then added and subtracted it from the sample mean, resulting in a confidence interval of approximately (6.1331, 6.8669).

Explanation:

To construct a 95% confidence interval for the average time spent in a particular job at General Motors, we utilize the sample mean, standard deviation, and the sample size to compute the margin of error and the confidence interval. Given that the sample mean is 6.5 years and the standard deviation is 1.7 years with a sample size of 85, we can calculate the confidence interval as follows:

This confidence interval suggests that we are 95% confident that the true average time spent in the job before promotion at General Motors lies between approximately 6.1 and 6.9 years.

Approximately 55.39% of females would not meet a college requirement of scoring at least 1025 on the SAT. This is found by calculating the z-score for the minimum required score and looking up the corresponding percentile.

To answer this question, we need to calculate the z-score — a statistic that tells us how many standard deviations away a score is from the mean. This formula is Z = (X - μ) / σ, where X is the score, μ is the mean, and σ is the standard deviation.

In this case, X is 1025 (the minimum required score), μ is 998 (the average SAT score), and σ is 202 (the standard deviation). So the z-score is Z = (1025 - 998) / 202 = 0.1336.

This z-score is positive, which means the minimum required score for the college is above the average score. Next, we check a z-score table or use a statistical calculator to find the percentage of scores that fall below this z-score, which gives us the percentage of females not meeting the requirement. For Z = 0.1336, the percentage is approximately 55.39% (using a statistical calculator or z-table). Therefore, roughly 55.39% of females would not meet a college requirement of scoring at least 1025 on the SAT.

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To find the percentage of females who do not satisfy the minimum score requirement of 1025 on the SAT-I test, we calculate the z-score for the minimum score and find the area under the normal distribution curve. Approximately 55.22% of females do not satisfy the minimum score requirement.

To find the percentage of females who do not satisfy the minimum score requirement of 1025 on the SAT-I test, we need to calculate the z-score for the minimum score and then find the area under the normal distribution curve to the left of that z-score. The formula for calculating the z-score is z = (x - μ) / σ, where x is the minimum score, μ is the mean, and σ is the standard deviation. So, z = (1025 - 998) / 202 = 0.1337.

Next, we can use a z-table or a calculator to find the area under the normal distribution curve to the left of a z-score of 0.1337. The area represents the percentage of females who do not satisfy the minimum score requirement. Using a z-table, we can find that the area is approximately 0.5522 or 55.22%.

Therefore, approximately 55.22% of females do not satisfy the minimum score requirement of 1025 on the SAT-I test.

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Answer:

-$0.90

Step-by-step explanation:

There are only two possible outcomes, winning $23 (W) or losing $15 (L). Therefore:

[tex]P(W) + P(L) = 1[/tex]

The probability of the player making his next 3 free throws (P(W)) is:

[tex]P(W) = \frac{217}{302}*\frac{217}{302}*\frac{217}{302}\\P(W) = 0.37098[/tex]

The probability of the player NOT making his next 3 free throws (P(L)) is:

[tex]P(L) = 1 - P(W) = 1 - 0.37098\\P(L) = 0.62902[/tex]

Expected value (EV) is given by the payoff of each outcome multiplied by its probability:

[tex]EV = (23*0.37098) -(15*0.62902)\\EV = -\$0.90[/tex]

The expected value of the proposition is -$0.90

Answer:

  x > 6

Step-by-step explanation:

Subtract $1329 from both sides, then divide by $40.

  $1,329 + $40x > $1,569

  $40x > $240

  x > 6

Marie needs to save for more than 6 more weeks.

_____

Comment on the answer

The given inequality is written using the > symbol. Marie would have exactly enough to cover the projected cost after 6 weeks, but it is appropriate from a finance point of view for her to save more than the required amount. It will take more than 6 weeks for her to do that.

Answer:

The correct option is D) [tex]f'(t)-g'(t) > 0[/tex]

Step-by-step explanation:

Consider the provided information.

People are entering a building at a rate modeled by f (t) people per hour and exiting the building at a rate modeled by g (t) people per hour,

The change of number of people in building is:

[tex]h(x)=f(t)-g(t)[/tex]

Where f(t) is people entering in building and g(t) is exiting from the building.

It is given that "The functions f and g are non negative and differentiable for all times t."

We need to find the the rate of change of the number of people in the building.

Differentiate the above function with respect to time:

[tex]h'(x)=\frac{d}{dt}[f(t)-g(t)][/tex]

[tex]h'(x)=f'(t)-g'(t)[/tex]

It is given that the rate of change of the number of people in the building is increasing at time t.

That means [tex]h'(x)>0[/tex]

Therefore, [tex]f'(t)-g'(t)>0[/tex]

Hence, the correct option is D) [tex]f'(t)-g'(t) > 0[/tex]

The rate of change of the number of people in the building is increasing at time t and with the help of this statement the correct option is D).

Given :

The change of the number of people in the building is given by:

[tex]h(x) = f(t) - g(t)[/tex]

To determine the inequality, differentiate the above equation with respect to time.

[tex]h'(x)=f'(t)-g'(t)[/tex]

Now, it is given that the rate of change of the number of people in the building is increasing at time t. That means:

[tex]h'(x)>0[/tex]

[tex]f'(t)-g'(t)>0[/tex]

Therefore, the correct option is D).

For more information, refer to the link given below:

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Answer:

B is 22.12 degrees; ∠C is 57.88°; c=29.24

Step-by-step explanation:

So, first, it's important to draw a diagram of the triangle the problem is talking about (see  attached picture).

Once the triangle has been drawn, we can visualize it better and determine what to do. So first, we are going to find what the value of angle B is by using law of sines:

[tex]\frac{sin B}{b}=\frac{sin A}{a}[/tex]

which can be solved for angle B:

[tex]sin B=b\frac{sin A}{a}[/tex]

[tex] B= sin^{-1}(b\frac{sin A}{a})[/tex]

and substitute the values we already know:

[tex] B= sin^{-1}(13\frac{sin 100 ^{o}}{34})[/tex]

which yields:

B=22.12°

Once we know what the angle of B is, we can now find the value of angle C by using the fact that the sum of the angles of any triangle is equal to 180°. So:

A+B+C=180°

When solving for C we get:

C=180°-A-B

C=180°-22.12°-|00°=57.88°

So once we know what angle C is, we can go ahead and find the length of side c by using the law of sines again:

[tex]\frac{c}{sin C}=\frac{a}{sin A}[/tex]

and solve for c:

[tex]c=sin C \frac{a}{sin A}[/tex]

so we can now substitute for the values we already know:

[tex]c=sin(57.88^{o})\frac{34}{sin(100^{o})}[/tex]

which yields:

c=29.24

Answer:

[tex]F_{T}(t)=\frac{1}{2} +\frac{1}{2}(1-e^{-\lambda t})[/tex]

Step-by-step explanation:

The cumulative distribution function (CDF) F(x),"describes the probability that a random variableX with a given probability distribution will be found at a value less than or equal to x".

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

[tex]P(X=x)=\lambda e^{-\lambda x}[/tex]

We are interested on the cumulative distribution function (CDF) of Jane’s waiting time. Let T the random variable that represent the Jane’s waiting time, and t possible value for the random variable T.

For [tex]t\geq 0[/tex] the CDF for the waiting time is given by:

[tex]F_{T}(t) =P(T\leq t)[/tex]

For this case we can use the total rule of probability and the conidtional probability. We have two options, find 0 or 1 customer ahead of Jane, and for each option we have one possibility in order to find the CDF, like this:

[tex]F_{T}(t)=P(T\leq t|0 customers)P(0 customers)+ P(T\leq t|1 customers)P(1 customers)[/tex]

On this case the probability that we need to wait if we have o customers ahead is [tex]P(T\leq t|0 customers)=1[/tex] since if we don't have a customer ahead, so on this case Jane will not wait. And assuming that the probability of find 0 or 1 customers ahead of Jane is equal we have [tex]P(0 customers)=P(1 customers)=\frac{1}{2}[/tex]. And replacing we have:

[tex]F_{T}(t)=\frac{1}{2} +\frac{1}{2}\int_{0}^{t} \lambda e^{-\lambda \tau} d\tau = \frac{1}{2}+\frac{1}{2}[-e^{-\lambda t}+e^{-\lambda 0}]= \frac{1}{2} +\frac{1}{2}(1-e^{-\lambda t})[/tex]

Jane's waiting time scenario can be split into two cases, when there are no customers ahead of her, and when there is one customer ahead of her. For these two cases, the Cumulative Distribution Function (CDF) of Jane's waiting time can be calculated as [tex]0.5 + 0.5 \times (1 - e^{-\lambda w})[/tex]. This answer is derived using the law of total probability and the definition of the CDF for the exponential distribution.

The question asks for the cumulative distribution function (CDF) of Jane’s waiting time at the bank. This is a probability question related to the exponential distribution and cumulative distribution function. The situation can be represented using two sub-situations: one, when there is no customer ahead (happens with 0.5 probability), Jane has no waiting time, and two, when there is a customer (happens with 0.5 probability) and Jane has to wait for an exponentially distributed time with parameter λ.

The cumulative distribution function (CDF) of an exponential random variable is given by [tex]F(x) = 1 - e^{-\lambda x}[/tex] when x ≥ 0. Using the law of total probability, the cumulative distribution function (CDF) of Jane's waiting time W can be obtained as  [tex]P(W \leq w) = P(0 \text{ customer}) \cdot P(W \leq w | 0 \text{ customer}) + P(1 \text{ customer}) \cdot P(W \leq w | 1 \text{ customer}) = 0.5 \cdot 1 + 0.5 \cdot (1 - e^{-\lambda w})[/tex]when w ≥ 0. Or in other words, Jane's waiting time has a CDF of [tex]0.5 + 0.5 \times (1 - e^{-\lambda w})[/tex]

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Answer:

a) 0.0176 or 1.76%

b) 0.2270 or 22.70%

c) 0.6268 or 62.68%

Step-by-step explanation:

Democrats: P(D) = 39%

Republicans: P(R) = 26%

Others: P(O) = 7%

Independent: P(I) = 100-39-26-7 =28%

a) Probability of talking to all​ Republicans in three calls:

[tex]P(N_R=3) =P(R)*P(R)*P(R)\\P(N_R=3) =0.26^3 = 0.0176[/tex]

a) Probability of talking to no democrats in three calls:

[tex]P(N_D=0) =(1-P(D)*(1-P(D)*(1-P(D)\\P(N_D=0) =(1-0.39)^3 = 0.2270[/tex]

c) Probability of talking to at least one independent in three calls:

[tex]P(N_I\geq1)=1-P(N_I=0)\\P(N_I\geq1) = 1-(1-0.28)*(1-0.28)*(1-0.28)\\P(N_I\geq1) = 0.6268[/tex]

a) The probability of talking to all Republicans in the first three calls is 1.7576%. b) The probability of talking to no Democrats in the first three calls is 22.6981%. c) The probability of talking to at least one Independent is 19.5643%.

a) To find the probability of talking to all Republicans in the first three calls, we need to multiply the probability of talking to a Republican on each call. The probability of talking to a Republican on the first call is 26%, on the second call is also 26%, and on the third call is still 26%. Therefore, the probability of talking to all Republicans in the first three calls is 0.26 * 0.26 * 0.26 = 0.017576 or 1.7576%.

b) To find the probability of talking to no Democrats in the first three calls, we need to multiply the probability of not talking to a Democrat on each call. The probability of not talking to a Democrat on the first call is 1 - 39% = 61%, on the second call is also 61%, and on the third call is still 61%. Therefore, the probability of talking to no Democrats in the first three calls is 0.61 * 0.61 * 0.61 = 0.226981 or 22.6981%.

c) To find the probability of talking to at least one Independent, we need to subtract the probability of not talking to any Independents from 1. The probability of not talking to an Independent on the first call is 1 - 7% = 93%, on the second call is also 93%, and on the third call is still 93%. Therefore, the probability of not talking to any Independents in the first three calls is 0.93 * 0.93 * 0.93 = 0.804357 or 80.4357%. Since we want the probability of talking to at least one Independent, we subtract this result from 1: 1 - 0.804357 = 0.195643 or 19.5643%.

Answer:

A. 2.5 standard deviations below the average salary.

Step-by-step explanation:

Hello!

Usually, when you calculate a probability of an X₀ value from a normally distributed variable you need to standardize it to reach the proper value. In this case, you already have the Z-value and need to reverse the standardization to obtain the X₀ value.

Z= X₀ - μ

δ

δ*Z = X₀ - μ

X₀= (δ*Z) + μ

replace Z= -2.50

X₀= (δ*-2.50) + μ

X₀= μ - (δ*2.50)

You can replace the Z value any time. I've just choose to do it at the end because it's more confortable for me.

I hope it helps!

Answer:

The Riemann Sum for [tex]\int\limits^5_4 {x^2+4} \, dx[/tex] with n = 4 using midpoints is about 24.328125.

Step-by-step explanation:

We want to find the Riemann Sum for [tex]\int\limits^5_4 {x^2+4} \, dx[/tex] with n = 4 using midpoints.

The Midpoint Sum uses the midpoints of a sub-interval:

[tex]\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f\left(\frac{x_0+x_1}{2}\right)+f\left(\frac{x_1+x_2}{2}\right)+f\left(\frac{x_2+x_3}{2}\right)+...+f\left(\frac{x_{n-2}+x_{n-1}}{2}\right)+f\left(\frac{x_{n-1}+x_{n}}{2}\right)\right)[/tex]

where [tex]\Delta{x}=\frac{b-a}{n}[/tex]

We know that a = 4, b = 5, n = 4.

Therefore, [tex]\Delta{x}=\frac{5-4}{4}=\frac{1}{4}[/tex]

Divide the interval [4, 5] into n = 4 sub-intervals of length [tex]\Delta{x}=\frac{1}{4}[/tex]

[tex]\left[4, \frac{17}{4}\right], \left[\frac{17}{4}, \frac{9}{2}\right], \left[\frac{9}{2}, \frac{19}{4}\right], \left[\frac{19}{4}, 5\right][/tex]

Now, we just evaluate the function at the midpoints:

[tex]f\left(\frac{x_{0}+x_{1}}{2}\right)=f\left(\frac{\left(4\right)+\left(\frac{17}{4}\right)}{2}\right)=f\left(\frac{33}{8}\right)=\frac{1345}{64}=21.015625[/tex]

[tex]f\left(\frac{x_{1}+x_{2}}{2}\right)=f\left(\frac{\left(\frac{17}{4}\right)+\left(\frac{9}{2}\right)}{2}\right)=f\left(\frac{35}{8}\right)=\frac{1481}{64}=23.140625[/tex]

[tex]f\left(\frac{x_{2}+x_{3}}{2}\right)=f\left(\frac{\left(\frac{9}{2}\right)+\left(\frac{19}{4}\right)}{2}\right)=f\left(\frac{37}{8}\right)=\frac{1625}{64}=25.390625[/tex]

[tex]f\left(\frac{x_{3}+x_{4}}{2}\right)=f\left(\frac{\left(\frac{19}{4}\right)+\left(5\right)}{2}\right)=f\left(\frac{39}{8}\right)=\frac{1777}{64}=27.765625[/tex]

Finally, use the Midpoint Sum formula

[tex]\frac{1}{4}(21.015625+23.140625+25.390625+27.765625)=24.328125[/tex]

This is the sketch of the function and the approximating rectangles.

Answer: [tex]\mu_x=18\text{ hours}[/tex]

[tex]\sigma_x=4\text{ hours}[/tex]

Step-by-step explanation:

We know that mean and standard deviation of sampling distribution is given by :-

[tex]\mu_x=\mu[/tex]

[tex]\sigma_x=\dfrac{\sigma}{\sqrt{n}}[/tex]

, where [tex]\mu[/tex] = population mean

[tex]\sigma[/tex] =Population standard deviation.

n= sample size .

In the given situation, we have

[tex]\mu=18\text{ hours}[/tex]

[tex]\sigma=6\text{ hours}[/tex]

n= 2

Then, the expected mean and the standard deviation of the sampling distribution will be :_

[tex]\mu_x=\mu=18\text{ hours}[/tex]

[tex]\sigma_x=\dfrac{\sigma}{\sqrt{n}}=\dfrac{6}{\sqrt{2}}=4.24264068712\approx4[/tex]  [Rounded to the nearest whole number]

Hence, the the expected mean and the standard deviation of the sampling distribution :

[tex]\mu_x=18\text{ hours}[/tex]

[tex]\sigma_x=4\text{ hours}[/tex]

Answer:

(1) 0.4207

(2) 0.7799

Step-by-step explanation:

Given,

Mean value,

[tex]\mu = 15.0[/tex]

Standard deviation,

[tex]\sigma = 1.25[/tex]

(1) P(X ≥ 17.5) = 1 - P( X ≤ 17.5)

[tex]= 1- P(\frac{x-\mu}{\sigma} \leq \frac{17.5-\mu}{\sigma})[/tex]

[tex]=1-P(z\leq \frac{17.5 - 15}{1.25})[/tex]

[tex]=1-P(z\leq \frac{2.5}{1.25})[/tex]

[tex]=1-P(z\leq 2)[/tex]

[tex]=1- 0.5793[/tex]   ( By using z-score table )

= 0.4207

(2) P(14 ≤ X ≤ 18) = P(X ≤ 18) - P(X ≤ 14)

[tex]=P(z\leq \frac{18 - 15}{1.25}) - P(z\leq \frac{14 - 15}{1.25})[/tex]

[tex]=P(z\leq \frac{3}{1.25}) - P(z\leq -\frac{1}{1.25})[/tex]

[tex]=P(z\leq 2.4) - P(z\leq -0.8)[/tex]

= 0.9918 - 0.2119

= 0.7799

The probabiliity that the force is greater than 17.5 kips is 2.28% while the probabiliity that the force is between 14 and 18 kips is 20.37%

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean) / standard deviation

Mean value 15.0 (kips) and standard deviation 1.25 (kips).

1) For 17.5:

z = (17.5 - 15) / 1.25 = 2

P(x > 17.4) = 1 - P(z < 2) = 1 - 0.9772 = 0.0228

2) For 14:

z = (14 - 15)/1.25 = 0.8

For 18:

z = (18 - 15)/1.25 = 2.4

P(14 < x < 18) = P(z < 2.4) - P(z < 0.8) = 0.9918 - 0.7881 = 0.2037

The probabiliity that the force is greater than 17.5 kips is 2.28% while the probabiliity that the force is between 14 and 18 kips is 20.37%

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Answer:

a) $430

b) -$90

Step-by-step explanation:

Given a random variable X with possible values

[tex]\large x_1,x_2,...x_n[/tex]

with respective probabilities of occurrence  

[tex]\large P(x_1),P(x_2),...P(x_n)[/tex]

then the expected value E(X) of X is

[tex]\large x_1*P(x_1)+x_2*P(x_2)+...+x_n*P(x_n)[/tex]

a)

The expected collision payment would then be

0*0.85 + 500*0.04 + 1000*0.04 + 3000*0.03 + 5000*0.02 + 8000*0.01 + 10000*0.01 = $430

So the insurance premium that would enable the company to break even is $430

b)

The expected value of the collision policy for a policyholder is the expected payments from the company minus the cost of coverage:

$430 - $520 = -$90

Why does the policyholder purchase a collision policy with this expected value?

Because the policyholder does not know what the probability of having an accident is in her particular case.

Besides, it is better to have the policy and not need it than to need it and not have it.

The probability computed shows that the collision insurance premium that would enable the company to break even is $430.

The collision insurance premium that would enable the company to break even will be calculated thus:

= (0 × 0.85) + (500 × 0.04) + (1000 × 0.04) + (3000 × 0.03) + (5000 × 0.02) + (8000 × 0.01 + (10000 × 0.01)

= $430

The expected value of the collision policy for a policyholder will be:

= $430 - 520

= -$90

In conclusion, the policyholder purchase a collision policy with this expected because he doesn't know the probability of having an accident.

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Answer:

Option b is right

Step-by-step explanation:

Given that  a sociologist is interested in testing if the average age at puberty of girls living is Thailand is different from the average age of puberty of girls living in Japan. To test her theory, she selects a random sample of 50 young Thai women and 50 young Japanese women and determines that the average age at puberty of the women in Japan is 1.7 years younger than the average age at puberty of the Thai women

If average of Japanese women is decreased by 0.8 years, we would get mean difference = [tex]1.7+0.8=2.5[/tex]

Since mean difference increases test statistic would increase thus reducing p value, i.e. chances of rejecting H0 higher.

The sample std devition would not change because of this.

The researcher would need a sample size of 271 individuals to be 90% confident that the sample proportion will not differ from the true proportion of adults

How to find the sample size ?

To determine the sample size needed to estimate the proportion of the adult population of the United States with high blood pressure with a 90% confidence level and a margin of error (precision) of 5%, you can use the formula for sample size for estimating proportions. The formula is:

[tex]\[n = \frac{Z^2 \cdot p(1-p)}{E^2}\][/tex]

E is the margin of error as a proportion (in this case, 5% or 0.05).

Plug in the values:

[tex]\(n = \frac{(1.645)^2 \cdot 0.5(1-0.5)}{(0.05)^2}\)[/tex]

[tex]\(n = \frac{2.706025 \cdot 0.25}{0.0025}\)[/tex]

[tex]\(n = \frac{0.67650625}{0.0025}\)[/tex]

n = 270.6025

= 271 people

Answer:

Dependent

Step-by-step explanation:

Given that there are 15 balls in an urn. 7 of the balls are red, and 8 of the balls are blue

when we do with replacement each time probability for red or blue remains the same.

a)  the probability that if you draw one ball, it will be blue=[tex]\frac{8}{15}[/tex]

(b) If you draw two balls without replacement,  the probability that you draw a red and then a blue

=[tex]\frac{7}{15} *\frac{8}{14} \\=\frac{4}{15}[/tex]

(c) If you draw two balls with replacement,  the probability that you draw a red and then a blue

=[tex]\frac{7}{15} *\frac{8}{15} \\=\frac{56}{225}[/tex]

(d) If you draw three balls without replacement,  the probability that you draw at least two red balls

=P(2 red, 1 blue)+P(3 blue)

=[tex]\frac{7C2*8C1}{15C3} +\frac{7C3}{15C3} \\=\frac{203}{455} =\frac{29}{65}[/tex]

(e) If you draw three balls with replacement,  the probability that you draw at least two red balls

= P(X≥2) where x is binomial with n=3 and p = 7/15

= 0.4506

(f) We play a game where I draw a ball first without replacement, and then you draw one. I draw a blue ball, and then you draw a red ball.

No when first ball is drawn without replacement the next probability for blue and red would be changed.  So dependent.

The probability of various scenarios involving drawing balls from an urn is calculated, including with and without replacement. The events of drawing a blue ball and a red ball after each other are examined in terms of their independence.

In order to answer the given question, we need to calculate the probability for each scenario:

(a) The probability of drawing a blue ball with replacement is

8/15

.

(b) The probability of drawing a red and then a blue ball without replacement is

(7/15) * (8/14)

.

(c) The probability of drawing a red and then a blue ball with replacement is

(7/15) * (8/15)

.

(d) The probability of drawing at least two red balls without replacement can be calculated by finding the probability of drawing two red balls and the probability of drawing three red balls, and then adding them together:

(7/15) * (6/14) + (7/15) * (6/14) * (5/13)

.

(e) The probability of drawing at least two red balls with replacement can be calculated by finding the probability of drawing two red balls and the probability of drawing three red balls, and then adding them together:

(7/15) * (7/15) + (7/15) * (7/15) * (7/15)

(f) No, the events of you drawing a blue ball and the student drawing a red ball after that are

not independent

because drawing the blue ball affects the probability of drawing a red ball for the student.

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Answer:

narrower, reduced

Step-by-step explanation:

Given that a sample of a given size is used to construct a 95% confidence interval for the population mean with a known population standard deviation

we have confidence interval is margin of error on either side of mean.

Margin of error= Critical value * std error

Std error in turn is inversely proportinal to square root of n

For same confidence level, if sample size is increased we get a less margin of error and hence a narrower confidence interval.

when a confidence interval is narrowed, probability of making a type I error would be reduced.

Hence we get

If a bigger sample had been used instead, then the 95% confidence interval would have been __narrower______ and the probability of making an error would have been ___reduced_____.

A larger sample size would result in a narrower 95% confidence interval and a decreased probability of making an error. This is due to less variability and increased precision with increased sample size.

If a larger sample size had been used to construct a 95% confidence interval for the population mean, the interval would have been narrower. This is because larger sample sizes typically result in less variability. In fact, as the sample size increases, the estimate of the population mean becomes more accurate, and thus the confidence interval around that estimate becomes tighter, containing less of the probability distribution.

The probability of making an error, or in other words, the margin of error, decreases with an increase in sample size. This reduction in the level of uncertainty is due to reduced variability seen with larger samples. By using a larger sample, the chances of the confidence interval not containing the population mean, thus making an error, decrease.

To give an example, if you initially have a 95% confidence interval of (67.02, 68.98) from a smaller sample and you then generate a bigger sample, you could get a confidence interval like (67.18, 68.82). This interval is narrower, representing the reduced variability and increased precision from the larger sample size.

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Answer: A bag can weigh 13.77 ounces and not need to be repacked.

Step-by-step explanation:

Since we have given that

Mean = 12.08 ounces

Standard deviation = 1.03 ounces

Bags in the upper 5% are too heavy and must be repackaged.

Using the standard normal table.

z = 1.645

So, [tex]X=\mu+z\sigma\\\\X=12.08+1.645\times 1.03\\\\X=13.77\ ounces[/tex]

Hence, A bag can weigh 13.77 ounces and not need to be repacked.

Answer:

a) [tex]\hat \mu =\bar X=24.694[/tex]

b) The 99% confidence interval would be given by (24.409;24.979)

c) Since the 99% confidence interval not contains the exposed to ambient temperatures of 24 degrees Celsius, and since the animals "that can maintain a body temperature different from the surroundings would be considered evidence of this regulating capability", on this case we can conclude that the sea crabs are able to regulate their body temperature.

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Data: 24.33, 24.61, 24.67, 24.64, 24.42, 24.97, 25.23, 24.73, 24.90, 24.44

[tex]\bar X[/tex] represent the sample mean  

[tex]\mu[/tex] population mean (variable of interest)

s represent the sample standard deviation

n=10 represent the sample size  

Part a

A point of estimate for the population mean is the sample mean, given by this formula:

[tex]\bar X= \frac{\sum_{i=1}^n x_i}{n}[/tex]

If we apply this formula we got that [tex]\hat \mu =\bar X=24.694[/tex]

Part b

In order to calculate the confidence interval first we need to calculate the sample deviation given by this formula:

[tex]s=\frac{\sum_{i=1}^n (x_i -\bar x)}{n-1}[/tex]

If we use this formula we got that [tex]s=0.277[/tex]

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)  

In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:

[tex]df=n-1=10-1=9[/tex]

Since the Confidence is 0.99 or 99%, the value of [tex]\alpha=0.01[/tex] and [tex]\alpha/2 =0.005[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,9)".And we see that [tex]t_{\alpha/2}=3.25[/tex]

Now we have everything in order to replace into formula (1):

[tex]24.694-3.25\frac{0.277}{\sqrt{10}}=24.409[/tex]    

[tex]24.694+3.25\frac{0.277}{\sqrt{10}}=24.979[/tex]

So on this case the 99% confidence interval would be given by (24.409;24.979)    

Part c

Since the 99% confidence interval not contains the exposed to ambient temperatures of 24 degrees Celsius, and since the animals "that can maintain a body temperature different from the surroundings would be considered evidence of this regulating capability", on this case we can conclude that the sea crabs are able to regulate their body temperature.

This is a one-sample z-test in statistics. You need to set null and alternative hypotheses, calculate the z-score, and compare it to the critical value to test if the mean score of second grade students in the school district significantly exceeds the nationwide average.

The subject matter here falls within Statistics, a branch of Mathematics. You want to test whether the mean score of second grade students in the school district is significantly greater than the nationwide average. To solve this, we perform a one-sample z-test, because we know the population standard deviation (σ = 15).

To start, we set the null hypothesis that the mean score for the district is equal to the nationwide average of μ0 = 50. The alternative hypothesis, according to the superintendent's belief, is that the mean score for the district is greater than 50.

You then calculate the z-score, which is the ratio of the difference between the sample mean and the population mean to the standard deviation of the population divided by the square root of the sample size (z = (X-bar - μ0) / (σ / √n). Here, X-bar is 52, n is 60 and σ is 15. After calculating the z-score, you would compare it to the critical z-value for the selected level of significance (typically 0.05 for a two-tailed test). If the calculated z score is larger than the critical z value, you would reject the null hypothesis and accept the alternative hypothesis, thus concluding that the second graders in the district have greater math skills than the nationwide average.

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Answer:

Step-by-step explanation:

The solid is a cuboid with length of 6 inches, a width of 3 inches, and a height of 2 inches.

The volume is l× w×h = 6×3×2 = 36inches^3

Therefore, the following statements are true about the Solid

1) The volume of the solid is 36 in.3.

2) The perimeter of one of its faces is 10 inches.(2width + 2 height = 2×2 + 2×3 = 10 inches)

3) The area of one of its faces is 6 inches^2. (width × height = 3×2 = 6 inches)

4) The area of one of its faces is 12 in.2.(length × height = 6×2 = 12 inches^2)

Answer : The correct options are:

The perimeter of one of its faces is 10 inches.

The area of one of its faces is 6 inch².

The area of one of its faces is 12 inch².

The volume of the solid is 36 inches³.

Step-by-step explanation :

Formula used for perimeter of one face (rectangle) is:

Perimeter = 2(l+b)

Perimeter = 2(b+h)

Perimeter = 2(l+h)

Formula used for area of one face (rectangle) is:

Area = l × b

Area = b × h

Area = l × h

Formula used for volume of solid (cuboid) is:

volume of solid = l × b × h

Given:

l = length = 6 inches

b = width = 3 inches

h = height = 2 inches

Now we have to calculate the perimeter of one face.

Perimeter = 2(l+b)

Perimeter = 2(6+3) = 18 inch

Perimeter = 2(b+h)

Perimeter = 2(3+2) = 10 inch

Perimeter = 2(l+h)

Perimeter = 2(6+2) = 16 inch

Now we have to calculate the area of one face.

Area = l × b

Area = 6 × 3 = 18 inch²

Area = b × h

Area = 3 × 2= 6 inch²

Area = l × h

Area = 6 × 2 = 12 inch²

Now we have to calculate the volume of solid.

volume of solid = l × b × h

volume of solid = 6 × 3 × 2

volume of solid = 36 inches³

The volume of solid is, 36 inches³

Answer:    

z=1.59

If we compare the p value and the significance level given [tex]\alpha=0.025[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we fail to reject the null hypothesis, so we can conclude that the mean repellency of the new bug repellent is greater than 89% at 0.025 of signficance.    

Step-by-step explanation:    

1) Data given and notation    

[tex]\bar X=0.92[/tex] represent the mean effectiveness of a new bug repellent for the sample    

[tex]\sigma=0.08[/tex] represent the population standard deviation for the sample    

[tex]n=18[/tex] sample size    

[tex]\mu_o =0.89[/tex] represent the value that we want to test  

[tex]\alpha=0.025[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)    

[tex]p_v[/tex] represent the p value for the test (variable of interest)

State the null and alternative hypotheses.    

We need to conduct a hypothesis in order to determine if the mean repellency of the new bug repellent is greater than 89% or 0.89, the system of hypothesis would be:    

Null hypothesis:[tex]\mu \leq 0.89[/tex]    

Alternative hypothesis:[tex]\mu > 0.89[/tex]    

We don't know the population deviation, and the sample size <30, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:    

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)    

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic    

We can replace in formula (1) the info given like this:    

[tex]t=\frac{0.92-0.89}{\frac{0.08}{\sqrt{18}}}=1.59[/tex]    

Calculate the P-value    

First we need to calculate the degrees of freedom given by:

[tex]df=n-1=18-1=17[/tex]

Since is a one-side upper test the p value would be:    

[tex]p_v =P(t_{17}>1.59)=0.065[/tex]

In Excel we can use the following formula to find the p value "=1-T.DIST(1.59;17;TRUE)"  

Conclusion    

If we compare the p value and the significance level given [tex]\alpha=0.025[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we fail to reject the null hypothesis, so we can conclude that the mean repellency of the new bug repellent is greater than 89% at 0.025 of signficance.    

Answer: d) one can be 90% confident that the mean drive through service time of this fast food chain is between 178.2 seconds and 181.6 seconds.

Step-by-step explanation:

The interpretation of 90% confidence interval says that a person can be 90% confident that the true population mean lies in it.

Given : A 90% confidence interval that results from examining 653 customers in one fast food chains drive through has a lower bound of 178.2 seconds and an upper bound of 181.6 seconds.

i.e.  90% confidence interval for population mean drive through service time of fast food restaurants is between 178.2 seconds and 181.6 seconds.

It means a person can be 90% confident that the mean drive through service time of this fast food chain is between 178.2 seconds and 181.6 seconds.

Hence, the correct answer is option d) .one can be 90% confident that the mean drive through service time of this fast food chain is between 178.2 seconds and 181.6 seconds.

Answer: y=x^2+2

Step-by-step explanation:

y=x^2+2 (answer choice 3) is parabolic and not linear

that is the answer