The length of time a person takes to decide which shoes to purchase is normally distributed with a mean of 8.54 minutes and a standard deviation of 1.91. Find the probability that a randomly selected individual will take less than 6 minutes to select a shoe purchase. Is this outcome unusual?

Answer:

(a) 25%

(b) 50%

(c) 18.75%

Step-by-step explanation:

Since there are two possible outcomes for each coin the number of total possible permutations is given by:

[tex]N=2*2*2*2=16[/tex]

(a) The first and last flips come up heads.

4 possible outcomes meet this requirement:

{HHHH}, {HHTH}, {HTHH},{HTTH}

P=4/16 = 25%

(b) There are at least two consecutive flips that come up heads.

8 possible outcomes meet this requirement:

{HHHH}, {HHHT},{HHTH} {HTHH},{THHH},{TTHH},{HHTT}, {THHT}

P=8/16 = 50%

(c) The first flip comes up tails and there are at least two consecutive flips that come up heads.

3 possible outcomes meet this requirement:

{THHH},{TTHH}, {THHT}

P=3/16 = 18.75%

Answer:

D. Because we would be interested in any difference between running on hard and soft surfaces, we should use a two-sided hypothesis test

Step-by-step explanation:

Hello!

When planning what kind of hypothesis to use, you have to take into account any other studies that were made about that topic so that you can decide the orientation you will give them.

Normally, when there is no other information available to give an orientation to your experiment, the first step to take is to make a two-tailed test, for example, μ₁=μ₂ vs. μ₁≠μ₂, this way you can test whether there is any difference between the two stands. Only after having experimental evidence that there is any difference between the treatments is there any sense into testing which one is better than the other.

I hope you have a SUPER day!

Answer:

The sum of squares due to regression(SSR)=928.02

Step-by-step explanation:

We are given that

Dependent variable=y

Independent variable=x

[tex]\sum x=90[/tex]

[tex]\sum(y-\bar y)(x-\bar x)=466[/tex]

[tex]\sum y=170[/tex]

[tex]\sum(x-\bar x)^2=234[/tex]

n=10

[tex]\sum(y-\bar y)^2=1434[/tex]

SSE=505.98

We have to find the sum of squares due to regression.

It means we have to find SSR.

SST=[tex]\sum(y-\bar y)^2=1434[/tex]

[tex]SSR=SST-SSE=1434-505.98=928.02[/tex]

Hence, the sum of squares due to regression(SSR)=928.02

Answer:

77.53

Step-by-step explanation:

Sample size (n) = 15

Sample mean (μ) = 75

Sample variance (V) = 25

Sample standard deviation (σ) = 5

For a 95% confidence interval, z-score = 1.960

The upper limit of the confidence interval is defined as:

[tex]UL=\mu+z\frac{\sigma}{\sqrt{n}}\\UL=75+1.960\frac{5}{\sqrt{15}} \\UL = 77.53[/tex]

Therefore, the upper limit of the 95% confidence interval proposed is 77.53.

The upper limit of a 95% confidence interval for the population mean is approximately 76.98.

The upper limit of a 95% confidence interval for the population mean can be calculated using the formula:

Upper Limit = Sample Mean + (Z-value)(Standard Error)

In this case, since the sample size is 15 and the sample variance is 25:

Standard Error = sqrt(sample variance/sample size)

Z-value can be obtained from the standard normal distribution table or calculator based on the desired confidence level. For a 95% confidence level, the Z-value is approximately 1.96.

Plugging in the values:

Upper Limit = 75 + (1.96)(sqrt(25/15))

Upper Limit ≈ 76.98

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Answer:

C. convenience sample

Step-by-step explanation:

Convenience sampling is a type of non-probability sampling or non-random sampling which is any sampling method where some elements of the population have no chance of selection. The selection is left at the judgment of the interviewer or investigator and this non-randomness in the statistical sense implies that the interviewer or investigator do not fulfill some of the basic requirements or assumptions of the common standard methods for testing hypothesis and drawing inferences from the sample data to the target population

Answer:

Step-by-step explanation:

Hello!

You have the difference between two sample means. Remember the sample means are variables with certain distribution, let's say, in this case, both sample means have a normal distribution. X[bar] = sample mean

X₁[bar]~N(μ₁;σ₁²/n₁)

X₂[bar]~N(μ₂;σ₂²/n₂)

Then the difference between these two variables results in a third variable that will also have a normal distribution:

X₁[bar]-X₂[bar]~N(μ₁-μ₂;σ₁²/n₁+σ₂²/n₂)

These are some of the properties of the normal distribution

Centered in μ

Symmetrical

Bell-shaped

[μ - σ; μ + σ]= 68% of the distribution

[μ - 2σ; μ+ 2σ]= 95% of the distribution

[μ - 3σ; μ+ 3σ]= 99.7% of the distribution

Check attachment.

Taking these properties into account, if you where to draw the results of the 100 trials, where μ₁-μ₂=0 would be its center and the standard deviation of the difference is 1.78.

68% of the information will be between (μ₁-μ₂) ± [(σ₁/√n₁)+(σ₂/√n₂)], this is 0 ± 1.78

I hope it helps!

Answer:

Part A: The population are the American adult citizens, excluding the ones from Alaska and Hawaii. The population is the people which the sample is trying to represent, as a hole.

The sample is a portion of this population, and in this case is represented by a randomly selected amount of people whose response to the interview has been selected.

Part B: The sample here has been selected in two steps. The first step is the one that we must pay attention to: the numbered list of one million responses from around the US (excluding Alaska and Hawaii). Because these responses were obtained by an online survey, the sample looks like a convenience sampling, as it depends on the availability and willingness from participants to take part of the study (is not compulsory for everyone, so not everyone is going to response, then there are people that is not going to be represented by). The second step is the random selection of a part of the previous responses. This last part will ensure that, the individuals that took part of the group that was interviewed, are well represented in the results.

Part C: As it was mentioned, there is a selection bias, because the information from the sample comes from a specific group of people that has certain features that may not represent all American adults citizens. For example, the opinion of  those people who do not use internet, will not be considered (and they may be a large number of persons). This situations weaken the conclusions obtained in the study, as they are not representative of the hole population.

Answer: 1.4375

Step-by-step explanation:

Pela has 5 3/4 feet of string to make necklaces. We would convert 5 3/4 feet to improper fraction. It becomes 23/4 feet. So Pela has 23/4 feet of string to make necklaces.

She wants to make 4 necklaces that are the same length. To determine how long should each necklace be,

We would divide the total length of the string by the number of necklaces to be made. It becomes

23/4 ÷ 4 = 23/4 × 1/4 = 23/16

The length of each string is 23/16 or 1.4375 feet

Answer:

The proof is wrong. The part that says 'take an element b ∈ A such that (a, b) ∈ R' is assuming that such an element b exists, and that may not be the case.  We can give the 'theorem' validation by adding the hypothesis ' each element of A is related to any other element of A', otherwise the 'theorem' is false. An example for that is the following relation on the natural numbers:

'a R b if both numbers are even'

This relation if crearly symmetric and transitive, but it is not reflexive, an odd number does not relate with itself. In fact, odd numbers dont relate with any number.

Final answer:

The error in the given "proof" lies in the assumption that an element b ∈ A exists such that (a, b) ∈ R, which is not necessarily true for all a ∈ A. Symmetry and transitivity of a relation R do not inherently guarantee its reflexivity.

Explanation:

The error in the "proof" that a symmetric and transitive relation R on a set A is also reflexive lies in the initial assumption. The proof assumes the existence of an element b ∈ A such that (a, b) ∈ R for an arbitrary a ∈ A, but this is not guaranteed. Reflexivity requires that (a, a) ∈ R for all a ∈ A, independently of the existence of any such b. The proof fails because it assumes a specific relationship exists (between a and b) to demonstrate reflexivity, which is a general property that must hold without needing to reference any other elements.

The properties of reflexivity, symmetry, and transitivity define an equivalence relation. Symmetry and transitivity alone do not imply reflexivity. Therefore, the statement that a symmetric and transitive relation is reflexive is incorrect without additional assumptions about R.

Answer:

Step-by-step explanation:

a. The pidgeons/objects here are the cards and the pigeonholes/boxes here are the suits. We are trying to draw cards/pidgeon that have the same suits/pidgeonholes. Since there are 4 different suits, we need to draw at least 5 cards to guarantee 2 cards of the same suit.

b. Let there be 3 holes, which represent 3 pairs of number with sum equals to 7. They are:

- {1,6} as 1 + 6 = 7

- {2,5} as 2 + 5 = 7

- {3,4} as 3 + 4 = 7

You can see that if we pick randomly 4 numbers, we will always end up with 2 numbers in the same hole, which means there will be at least a pair and add up to 7.

Answer:

There is a 26.39% probability that the coin comes up heads and the die comes up less than 4 and the roulette wheel comes up with a number greater than 17.

Step-by-step explanation:

We have to find the probability of the three separate events, and then multiply them.

coin comes up heads

There is a [tex]\frac{1}{2}[/tex] probability that the coin comes up heads.

the die comes up less than 4

The are 15 sides on the die, from 0 to 14.

The values that satisfy us are 0,1,2,3.

So the probability is [tex]\frac{4}{15}[/tex].

the roulette wheel comes up with a number greater than 17

There roulette wheel can come from 1 to 36. There are 19 values greater than 17. So this probability is [tex]\frac{19}{36}[/tex]

What is the probability that the coin comes up heads and the die comes up less than 4 and the roulette wheel comes up with a number greater than 17 ?

[tex]P = \frac{1}{2}*\frac{4}{15}*\frac{19}{36} = 0.2639[/tex]

There is a 26.39% probability that the coin comes up heads and the die comes up less than 4 and the roulette wheel comes up with a number greater than 17.

The combined probability of the coin landing on heads, the die rolling less than 4, and the roulette wheel landing on a number greater than 17 is found by multiplying the individual probabilities of each event.

The question involves calculating the combined probability of independent events in a probability experiment: flipping a coin, rolling a 15-sided die, and spinning a roulette wheel. Each event's probability is calculated separately and then multiplied together to find the probability of all events occurring simultaneously.

The probability the coin comes up heads is 0.5, because a fair coin has two sides and the event has a theoretical probability of 1 in 2. When rolling a 15-sided die, the probability it comes up less than 4 (that is, obtaining a 1, 2, or 3) is 3 out of 15, as there are 3 favorable outcomes out of 15 possible outcomes. And for the roulette wheel, assuming it has numbers from 0 to 36, the probability of spinning a number greater than 17 is 19 out of 38, since there are 19 numbers from 18 to 36 (excluding 0 and 00 which might also be present).

To find the combined probability, you would multiply these probabilities together:

Combined Probability = Probability(Heads) * Probability(Die < 4) * Probability(Roulette > 17)
= 0.5 * (3/15) * (19/38)

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that Advandia is a drug used to treat diabetes, but it may cause an increase in heart attacks among a population already susceptible.

Sample size n =1`456

Sample proportion of persons having heart attack p1= 27/1456 = 0.0186

II sample

Size = 2895

p2 = sample proportion = 41/2895 = 0.0142

a) Not matched pair data but independent proportions

b)

Step 1:  [tex]H_0: p_1=p_2\\H_a: p_1 > p_2[/tex]

(right tailed test at 5% significance level)

Step 2:  Test statistic z = 1.0995

Step 3:  p value = 0.13567

Step 4:  Since p >0.05 accept null hypothesis.

There is no evidence to suggest that there is a significant increase in the proportion of people who suffer heart attacks when using Avandia compared to other treatments.

Step 5:

The P-value of 0.0072, we can conclude that there is statistically significant evidence to support the claim that the proportion of wives married less than two years who planned to have children is significantly higher than the proportion of wives married five years.

To determine whether the proportion of wives married less than two years who planned to have children is significantly higher than the proportion of wives married five years, we can conduct a hypothesis test, following these steps:

1. Define the null and alternative hypotheses:

Null hypothesis (H0): The proportion of wives planning to have children is the same in both groups, regardless of the length of marriage.

Alternative hypothesis (H1): The proportion of wives planning to have children is higher in the group married less than two years compared to the group married five years.

2. Calculate the proportions and standard errors:

Proportion of wives planning children (<2 years): 240/300 = 0.8

Proportion of wives planning children (5 years): 288/400 = 0.72

Pooled standard error: sqrt((0.8*(1-0.8))/300 + (0.72*(1-0.72))/400) = 0.0298

3. Calculate the test statistic:

z = (0.8 - 0.72) / 0.0298 = 2.68

4. Find the P-value:

Using a z-score table or statistical software, look up the P-value associated with z = 2.68. This gives us a P-value of approximately 0.0072.

5. Make a decision:

Typically, we use a significance level of alpha (α) = 0.05. Since the P-value (0.0072) is less than alpha, we reject the null hypothesis.

This means there is statistically significant evidence to conclude that the proportion of wives planning to have children is higher in the group married less than two years compared to the group married five years.

Therefore, based on the P-value of 0.0072, we can conclude that there is statistically significant evidence to support the claim that the proportion of wives married less than two years who planned to have children is significantly higher than the proportion of wives married five years.

Answer:

[tex]H_{0}: \mu \leq 63500\\H_A: \mu > 63500[/tex]

Step-by-step explanation:

We are given the following in the question:

The owner of a football team claims that the average attendance at games is over 63,500.

He wants to justify that the team needs to be moved to a larger stadium outside the city.

If the attendance is larger than 63,500 the team would be moved to a larger stadium and if it is less than or equal to 63,500 that it would not.

Thus, the null and alternate hypothesis will be designed as:

[tex]H_{0}: \mu \leq 63500\\H_A: \mu > 63500[/tex]

The null hypothesis says that the average attenders is equal to or less than 63,500 and alternate supports the claim that the attenders average is greater than 63,500.

Answer:

Step-by-step explanation:

8) looking at the figure at number 8,

It is a quadrilateral. In a quadrilateral, the opposite angles are supplementary. This means that the sum of all the angles is 360 degrees. We have assigned y degrees to the remaining unknown angle.

y = 180 - 71 = 109 degrees( this is because the sum of angles on a straight line is 180 degrees.

Therefore

10x + 6 + 8x - 1 + 13x - 2 + 109 = 360

31x + 112 = 360

31x = 360 - 112 = 248

x = 248/31 = 8

9) looking at the figure, we have assigned alphabets a, b and c to represent the inner angles that form the triangle.

a + 9x + 1 = 180

a = 180 - 1 -9x = 179 - 9x(this is because the sum of the angles on a straight line is 180 degrees)

b + 5x + 12 = 180

b = 180 - 12 - 5x

b = 168 - 5x

c + 10x -37 = 180

c = 180 - 10x + 37

c = 217 - 10x

a + b + c = 180( sum of angles in a triangle is 180 degrees)

179 - 9x + 168 - 5x + 217 - 10x = 180

-9x - 5x - 10x = 180 - 179 - 168 - 217

-24x = -384

x = -384/-24

x = 16

Answer: he drove 156 miles

Step-by-step explanation:

Aldo rented a truck for one day. There was a base fee of $20.99. This means that the fee of $20.99 is constant.

There was an additional charge of 86 cents for each mile driven.

Converting 86 cents to dollar, it becomes 86/100 = $0.86

Aldo had to pay $155.15

when he returned the truck. This means that the sum of the base fee and the additional fee is $155.15. The additional fee paid would be the total amount paid minus the base fee. It becomes

155.15 - 20.99 = 134.16

Since there is an additional charge of 0.86 for each mile driven, number of miles for which he was charged $134.16 will be total additional fee divided by cost per mile. It becomes

134.16/0.86 = 156 miles

The length of a curve [tex]C[/tex] given parametrically by [tex](x(t),y(t))[/tex] over some domain [tex]t\in[a,b][/tex] is

[tex]\displaystyle\int_C\mathrm ds=\int_a^b\sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]

In this case,

[tex]x(t)=\cos(\cos4t)\implies\dfrac{\mathrm dx}{\mathrm dt}=-\sin(\cos4t)(-\sin4t)(4)=4\sin4t\sin(\cos4t)[/tex]

[tex]y(t)=\sin(\cos4t)\implies\dfrac{\mathrm dy}{\mathrm dt}=\cos(\cos4t)(-\sin4t)(4)=-4\sin4t\cos(\cos4t)[/tex]

So we have

[tex]\displaystyle\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2=16\sin^24t\sin^2(\cos4t)+16\sin^24t\cos^2(\cos4t)=16\sin^24t[/tex]

and the arc length is

[tex]\displaystyle\int_0^1\sqrt{16\sin^24t}\,\mathrm dt=4\int_0^1|\sin4t|\,\mathrm dt[/tex]

We have

[tex]\sin(4t)=0\implies4t=n\pi\implies t=\dfrac{n\pi}4[/tex]

where [tex]n[/tex] is any integer; this tells us [tex]\sin(4t)\ge0[/tex] on the interval [tex]\left[0,\frac\pi4\right][/tex] and [tex]\sin(4t)<0[/tex] on [tex]\left[\frac\pi4,1\right][/tex]. So the arc length is

[tex]=\displaystyle4\left(\int_0^{\pi/4}\sin4t\,\mathrm dt-\int_{\pi/4}^1\sin4t\,\mathrm dt\right)[/tex]

[tex]=-\cos(4t)\bigg_0^{\pi/4}-\left(-\cos(4t)\bigg_{\pi/4}^1\right)[/tex]

[tex]=(\cos0-\cos\pi)+(\cos4-\cos\pi)=\boxed{3+\cos4}[/tex]

In this exercise we have to use the knowledge of the integral to calculate the length of the arc:

The length of a curve is given by  [tex]3+ cos( 4)[/tex]

The length of a curve  given parametrically by  [tex](x(t), y(t))[/tex] over some domain  is [tex]t \in [a, b][/tex]

[tex]\int\limits_C \, ds = \int\limits^a_b {\sqrt{(\frac{dx}{dt})^2 + (\frac{dy}{dt})^2 } } \, dt[/tex]

Now performing the derivatives with respect to X and Y, we find that:

[tex]x(t) = cos(cos4t) \rightarrow \frac{dx}{dt} = -sin(cos4t)(-sin4t)(4)= 4sin4tsin(cos4t)\\y(t) = sin(cos4t) \rightarrow \frac{dy}{dt} = cos(cos4t)(-sin4t)(4)=-4sin4tcos(cos4t)[/tex]

So we have:

[tex](\frac{dx}{dt} )^2+(\frac{dy}{dt} )^2= 16sin^24tsin^2(cos4t)+16sin^24tcos^2(cos4t)= 16sin^24t[/tex]

And the arc length is:

[tex]\int\limits^1_0 {\sqrt{16sin^24t} } \, dt= 4\int\limits^1_0 {sin4t} \, dt\\sin(4t)=0 \rightarrow 4t=n\pi \rightarrow t= \frac{n\pi }{4}[/tex]

where n  is any integer; this tells us  [tex]sin(4t)\geq 0[/tex] on the interval [tex][0,\pi/4][/tex] and  [tex]sin(4t)<0[/tex] on [tex][\pi/4, 1][/tex]. So the arc length is:

[tex]=4(\int\limits^{\pi/4}_0 {sin(4t)} \, dt - \int\limits^1_{\pi/4} {sin(4t)} \, dt)\\=(cos(0)-cos(\pi))+(cos(4)-cos(\pi))= 3+cos(4)[/tex]

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Answer: The study used a total of N 36 participants.

Step-by-step explanation:

There are 3 treatment conditions were compared in the study and the total number of participants in the study is 39.

Degree of freedom, in mathematics, any of the number of independent quantities necessary to express the values of all the variable properties of a system.

Given the ratio F(2, 36)

F takes in degree of freedom values; degree of freedom of groups ; degree of freedom of error

Hence,

df group or treatment = 2

df error = 36

df treatment = k - 1

k = Number of groups

2 = k - 1

k = 3

Number of treatment condition = 3

df error = N-k

N = total number of observations

36 = N - 3

N = 39

Hence, there are 3 treatment conditions were compared in the study and the total number of participants in the study is 39.

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Answer:

We conclude that the storm is not increasing above the severe rating.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 16.4 feet

Sample mean, [tex]\bar{x}[/tex] = 17.3 feet

Sample size, n = 34

Alpha, α = 0.01

Population standard deviation, σ = 3.5 feet

First, we design the null and the alternate hypothesis

[tex]H_{0}: \mu = 16.4\text{ feet}\\H_A: \mu > 16.4\text{ feet}[/tex]

We use One-tailed(right) z test to perform this hypothesis.

Formula:

[tex]z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]

Putting all the values, we have

[tex]z_{stat} = \displaystyle\frac{17.3 - 16.4}{\frac{3.5}{\sqrt{34}} } = 1.49[/tex]

Now, [tex]z_{critical} \text{ at 0.01 level of significance } = 2.33[/tex]

Since,  

[tex]z_{stat} < z_{critical}[/tex]

We fail to reject the null hypothesis and accept null hypothesis. Thus, the  the storm is not increasing above the severe rating.

The level of significance is 0.01 and the sample test statistic is 1.30.

The level of significance is given as ? = 0.01.

To test if the storm is increasing above the severe rating, we can calculate the z-score.

The formula for the z-score is: z = (x - ?) / (σ / √n), where x is the sample mean, ? is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, x = 17.3 feet, ? = 16.4 feet, σ = 3.5 feet, and n = 34 waves.

Plugging in these values into the formula, we get: z = (17.3 - 16.4) / (3.5 / √34) ≈ 1.30 (rounded to two decimal places).

The sample test statistic is 1.30.

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Answer:

P(Type ll error) = 0.2327

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 15 minutes

Sample size, n = 10

Alpha, α = 0.05

Population standard deviation, σ = 4 minutes

First, we design the null and the alternate hypothesis

[tex]H_{0}: \mu = 18\\H_A: \mu > 18[/tex]

We use One-tailed z test to perform this hypothesis.

Formula:

[tex]z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]

[tex]z_{critical} \text{ at 0.05 level of significance } = 1.645[/tex]

Putting the values, we get,

[tex]z_{stat} = \displaystyle\frac{\bar{x}- 15}{\frac{4}{\sqrt{10}} } > 1.645\\\\\bar{x} -1 5 > 1.645\times \frac{4}{\sqrt{10}}\\\\\bar{x} -15 > 2.08\\\bar{x} = 17.08[/tex]

Type ll error is the error of accepting the null hypothesis when it is not true.

P(Type ll error)

[tex]P(\bar{x}<17.07 \text{ when mean is 18})\\\\= P(z < \frac{\bar{x}-18}{\frac{4}{\sqrt{10}}})\\\\= P(z < \frac{17.08-18}{\frac{4}{\sqrt{10}}})\\\\= P(z<-0.7273)[/tex]

Calculating value from the z-table we have,

[tex]P(z<-0.7273) = 0.2327[/tex]

Thus,

P(Type ll error) = 0.2327

Answer:

13,8%

Step-by-step explanation:

There are six employees and six cheks, so there are 36 (6x6) possible combinations so if we need to measure the probability that five of them receive the exact check  is only one for each one of them over the 36 possibilities, so 1/36 for one plus 1/36 the second and so on.  5/36 = 13,8%.

Answer:

0

Step-by-step explanation:

If 5 of them are correct, then the 6th one will also be correct. Thus, it is impossible to have exactly 5 correct, therefore 0

Answer:

The 95% confidence interval would be given by (29.780;32.020)  

Step-by-step explanation:

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".

[tex]\bar X=30.9[/tex] represent the sample mean for the sample  

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

s=7.5 represent the sample standard deviation

n=174 represent the sample size  

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=174-1=173[/tex]

Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,173)".And we see that [tex]t_{\alpha/2}=1.97[/tex], this value is similar to the obtained with the normal standard distribution since the sample size is large to approximate the t distribution with the normal distribution.  

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

[tex]30.9-1.97\frac{7.5}{\sqrt{174}}=29.780[/tex]    

[tex]30.9+1.97\frac{7.5}{\sqrt{174}}=32.020[/tex]

So on this case the 95% confidence interval would be given by (29.780;32.020)    

The value 29.6 is not contained on the interval calculated.

Answer: a) 2002, b) 840, c) 10010.

Step-by-step explanation:

Since we have given that

Number of students = 14

Number of students senior = 8

Number of students junior = 6

(a) How many ways are there to select a committee of 5 students?

Here, n = 14

r = 5

We will use "Combination" for choosing 5 students from 14 students.

[tex]^{14}C_5=2002[/tex]

(b) How many ways are there to select a committee with 3 seniors and 2 juniors?

Again we will use "combination":

[tex]^8C_3\times ^6C_2\\\\=56\times 15\\\\=840[/tex]

(c) Suppose the committee must have five students (either juniors or seniors) and that one of the five must be selected as chair. How many ways are there to make the selection?

So, number of ways would be

[tex]^{14}C_5\times ^5C_1\\\\=2002\times 5\\\\=10010[/tex]

Hence, a) 2002, b) 840, c) 10010.

There are 2002 ways to select a committee of any 5 students, 840 ways to select a committee specifically with 3 seniors and 2 juniors, and 10010 ways to select a committee and designate one as chair.

The subject of this question is combinatorics, which is part of mathematics. It relates to counting, specifically concerning combinations and permutations. Combinations represent the number of ways a subset of a larger set can be selected, while permutations are the number of ways to arrange a subset.

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Answer:

- frequency of action potentials

The central nervous system determines the strength of a stimulus based on the frequency of action potentials. The intensity of the stimulus is interpreted not by the size, but by the frequency at which these potentials are produced.

The central nervous system determines the strength of a stimulus based on the frequency of action potentials. The central nervous system uses action potentials to transfer and process information. An action potential is a brief electrical charge that travels along an axon. The strength or intensity of the stimulus is interpreted not by the size of the action potentials, but by the frequency at which they are produced. For instance, a slightly warm temperature may produce action potentials at a lower frequency than a very hot temperature, which would produce action potentials at a high frequency. The central nervous system decodes this frequency to understand the intensity of the stimulus.

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We use the Z-score to determine the probability of selecting a single woman with a height less than 64.9 inches, and the concept of a sampling distribution (standard error) for a sample of 22 women. Generally, the larger the sample size, the closer the sample mean gets to the population mean, making it usually more probable to select one woman with a height of less than 64.9 inches than for a sample of 22 women.

This question is about probability and statistics, and specifically about the Normal Distribution and its applications. We know that the height of women aged 20-29 is normally distributed with a mean of 64.4 inches and a standard deviation of 2.3 inches.

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Calculate probabilities for selecting 1 woman and a sample of 22 women with heights less than 64.9 inches; Compare which selection is more likely.

Given:

Mean (μ) = 64.4 inches

Standard deviation (σ) = 2.3 inches

Calculate the z-score:

z = (x - μ) / σ

  = (64.9 - 64.4) / 2.3

  = 0.5 / 2.3

  = 0.2174

Now, we look up the probability corresponding to a z-score of 0.2174 in the standard normal table.

The probability for z = 0.2174 is approximately 0.5869.

So, the probability of randomly selecting 1 woman with a height less than 64.9 inches is approximately 0.5869.

Calculate standard error:

SE = σ / √n

    = 2.3 / √(22)

    ≈ 0.489

Find the z-score for the sample mean:

z = ([tex]^-_x[/tex] - μ) /  σ

 = (64.9 - 64.4) / 0.489

 = 0.5 / 0.489

 ≈ 1.021

Now, we look up the probability corresponding to a z-score of 1.021 in the standard normal table.

The probability for z = 1.021 is approximately 0.8451.

So, the probability of selecting a sample of 22 women with a mean height of less than 64.9 inches is approximately 0.8451.

→ Probability of randomly selecting 1 woman with a height less than 64.9 inches: 0.5869

→ Probability of selecting a sample of 22 women with a mean height less than 64.9 inches: 0.8451

Since 0.8451 is greater than 0.5869, it is more likely to select a sample of 22 women with a mean height of less than 64.9 inches.

Answer:

  see below

Step-by-step explanation:

The definition of a parallelogram is that opposite sides of the quadrilateral are parallel. Felice already knows one pair of opposite sides is parallel. By showing the slope of RQ is the same as the slope of ST, she can show the other pair of opposite sides is parallel, hence the figure is a parallelogram.

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The other answer choices are essentially nonsense.

Answer:

Top Right

Step-by-step explanation:

The function S(t) that represents the number of computers sold each month is S(t) = -18t^(5/3) + 2,440.

The company will continue to manufacture this computer for 5.656 months.

We have,

To find the function S(t), which represents the number of computers sold each month, we need to integrate the rate of change function S'(t).

Given:

S'(t) = -30t^(2/3)

Integrating S'(t) with respect to t will give us S(t):

∫S'(t) dt = ∫-30t^(2/3) dt

Using the power rule for integration:

S(t) = -30 * (3/5) * t^(5/3) + C

Simplifying:

S(t) = -18t^(5/3) + C

Now, we need to find the value of C, which represents the constant of integration.

Given that monthly sales at t = 0 (S(0)) are 2,440 computers, we can substitute this value into the equation:

S(0) = -18(0)^(5/3) + C

2,440 = 0 + C

C = 2,440

Substituting the value of C back into the equation, we get:

S(t) = -18t^(5/3) + 2,440

To find how long the company will continue to manufacture this computer, we need to solve for t when S(t) = 1,000:

-18t^(5/3) + 2,440 = 1,000

Simplifying the equation and rearranging:

-18t^(5/3) = -1,440

Dividing by -18:

t^(5/3) = 80

Taking the 3rd root of both sides to isolate t:

t = (80)^(3/5)

t  = 5.656

Therefore,

The function S(t) that represents the number of computers sold each month is S(t) = -18t^(5/3) + 2,440.

The company will continue to manufacture this computer for 5.656 months.

Learn more about integrations here:

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The function S(t) is obtained via integration of S'(t) with respect to t. We find that S(t) = -45t^(5/3) + 2440. When the computer sales fall to a 1000, it takes approximately 5.71 months, given the decline rate.

To find the function S(t) from its derivative, S'(t), we need to perform an integral of S'(t) which is -30t^(2/3). By performing the integral:

∫ S'(t)dt = ∫ -30t^(2/3) dt = -45t^(5/3) + C

Where C is the constant of integration.

To find C, we know from the question that at t=0, S(t) = 2440. So:
2440 = -45*(0)^(5/3) + C
2440 = C

Now we have the function: S(t) = -45t^(5/3) + 2440

We also know from the question that the company will stop manufacturing the computer when the monthly sales reach 1000 computers. We set our function equal to 1000 to find the time t:
1000 = -45t^(5/3) + 2440

We can solve for t and we get: t = ((2440-1000)/45)^(3/5), which is approximately 5.71 months.

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Answer:

More than 50% would germinate

Step-by-step explanation:

Given that in the production of a plant, a treatment is being evaluated to germinate seed. From a total of 60 seed it was observed that 37 of them germinated

Let us check whether more than 50% will germinate using hypothesis test

[tex]H_0: p = 0.50\\H_a: p>0.50\\[/tex]

(right tailed test)

Sample proportion p =[tex]\frac{37}{60} =0.617\\q = 0.383\\Std error = \sqrt{\frac{pq}{n} } =0.0628[/tex]

p difference = 0.117

Test statistic Z = p difference/std error = 1.864

p value =0.0312

Since p value <0.05 our significance level of 5% we reject null hypothesis

It is  possible to claim that most of the seed will germinate (i.e. more than 50%)

Answer:

Confidence Interval: (0.44,1.00)

Step-by-step explanation:

We are given the following data set:

0.60, 0.74, 0.09, 0.89, 1.31, 0.51, 0.94

Formula:

[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]  

where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.  

[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]

[tex]Mean =\displaystyle\frac{:5.08}{7} = 0.725[/tex]

Sum of squares of differences = 0.8809

[tex]S.D = \sqrt{\frac{0.8809}{6}} = 0.383[/tex]

90% Confidence interval:  

[tex]\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}[/tex]  

Putting the values, we get,  

[tex]t_{critical}\text{ at degree of freedom 6 and}~\alpha_{0.10} = \pm 1.943[/tex]  

[tex]0.725 \pm 1.943(\frac{0.383}{\sqrt{7}} ) =0.725 \pm 0.2812 = (0.44,1.00)[/tex]

No, it does not appear that there is too much mercury in tuna​ sushi.