find an explicit formula for the arithmetic sequence 10, -10, -30, -50, ...

Answer:

[tex]a) \ H_o:\hat p_f=\hat p_m\\\ \ \ H_a:\hat p_f\neq \hat p_m\\\\b) z\ test=2.925, \ p\ value(two-tail)=0.003444\\\\\\[/tex]

c)  Reject  H_o  since there is sufficient evidence to suggest that there is difference between males and females with respect to how they feel about this issue.

d. No. Interval does not include zero

e. [tex]CI=[0.01044<(\hat p_f-\hat p_m)<0.05576[/tex]

We are 95% confident that the proportional difference lies between the [0.010444,0.05576] interval.

Step-by-step explanation:

a. The null hypothesis is that there is no difference between males and females with respect to how they feel about this issue:

[tex]H_o:p_m=p_f[/tex]

-The alternative hypothesis is that there is some difference between males and females with respect to how they feel about this issue:

[tex]H_a:p_m\neq p_f[/tex]

where [tex]p_m, \ p_f[/tex] is the proportion of males and females respectively.

b. The proportion of males and females in the study can be calculated as follows:

[tex]\hat p=\frac{x}{n}\\\\\hat p_f=\frac{1729}{1913}=0.9038\\\\\hat p_m=\frac{1111}{1276}=0.8707[/tex]

[tex]\hat p=\frac{x_f+x_m}{n_m+n_f}=\frac{1111+1729}{1276+1913}=0.8906[/tex]

#We then calculate the test statistic using the formula:

[tex]z=\frac{(\hat p_f-\hat p_m)}{\sqrt{\hat p(1-\hat p)(\frac{1}{n_f}+\frac{1}{n_m})}}\\\\\\=\frac{(0.9038-0.8707)}{\sqrt{(0.8906\times0.1094)(\frac{1}{1913}+\frac{1}{1276})}}\\\\\\=2.9250\\\\\therefore p-value=0.001722\\[/tex]

[tex]\# The \ two \ tail \ p-value \ is\\\\=0.01722\times 2\\\\=0.003444[/tex]

c. Since p<0.05:

[tex]p<0.05\\\\0.00344<0.05\\\\\therefore Reject \ H_o[/tex]

Hence, we Reject the Null Hypothesis since there is sufficient evidence to suggest that there is difference between males and females with respect to how they feel about this issue

d. The 95% confidence interval can be calculated as below:

[tex]CI=(p_f-p_m)\pm z_{\alpha/2}\sqrt{\frac{\hat p_m(1-\hat p_m)}{n_m}+\frac{\hat p_f(1-\hat p_f)}{n_f}}\\\\=(0.9038-0.8707)\pm 1.96\sqrt{0.00008823+0.000045449}\\\\=0.03310\pm 0.02266\\\\=[0.01044,0.05576][/tex]

Hence, the confidence interval does not include  0

e. The 95% confidence interval calculated from above is :

[tex]0.01044<(p_f-p_m)<0.05576[/tex]

Hence, we are 95% confident that the proportional difference will fall between the interval [tex]0.01044<(\hat p_f-\hat p_m)<0.05576[/tex]

Answer:

a on edge2021

Step-by-step explanation:

The volume is One-fourth of the original.

"It is a three dimensional structure having two parallel bases joined by a curved surface, at a fixed distance."

V = π × r² × h, where 'r' is the radius of the circular base and 'h' is the height of the cylinder.

In the given question,

the radius of the cylinder is 10 cm, and the height is 14 cm.

⇒ r = 10 cm, h = 14 cm

The volume of the cylinder would be,

[tex]V_1=\pi\times 10^2\times 14\\\\V_1=\frac{22}{7}\times 100 \times 14\\\\V_1=4400~~cu.~cm.[/tex]

If the radius is halved, the radius becomes 5 cm.

The new volume of a cylinder would be,

[tex]V_2=\pi \times 5^2\times 14\\\\V_2=\frac{22}{7}\times 25 \times 14\\\\V_2=1100~~cu.~cm.[/tex]

The ratio between the original and the new volume of the cylinder is:

[tex]\Rightarrow \frac{1100}{4400}=\frac{1}{4}\\\\\Rightarrow V_2=\frac{1}{4}V_2[/tex]

This means, the volume is One-fourth of the original.

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Answer:

a)

USL = 6.2 inches

LSL = 5.8 inches

b) Cp = 1.33

Cpk = 0.67

c)

Yes it meets all specifications

Step-by-step explanation:

The specification for a plastic handle calls for a length of 6.0 inches ± .2 inches. The standard deviation of the process is estimated to be 0.05 inches. What are the upper and lower specification limits for this product? The process is known to operate at a mean thickness of 6.1 inches. What is the Cp and Cpk for this process?   Is this process capable of producing the desired part?

Given that:

Mean (μ) = 6.1 inches, Standard deviation (σ) = 0.05 inches and the length of the plastic handle is 6.0 inches ± .2

a) Since the length of the plastic handle is 6.0 inches ± .2  = (6 - 0.2, 6 + 0.2)

The Upper specification limits (USL) = 6 inches + 0.2 inches = 6.2 inches

The lower specification limits (LSL) = 6 inches - 0.2 inches = 5.8 inches

b) The Cp is given by the formula:

[tex]Cp=\frac{(USL-LSL)}{6\sigma} =\frac{(6.2-5.8)}{6*0.05} =1.33[/tex]

The Cpk is given by the formula:

c)

The upper specification limit lies about 3 standard deviations from the centerline, and the lower specification limit is further away, so practically all units will meet specifications

[tex]Cpk=min(\frac{USL-\mu}{3\sigma},\frac{\mu -LSL}{3\sigma})=min(\frac{6.2-6.1}{3*0.05},\frac{6.1-5.8}{3*0.05})=min(0.67,2)=0.67[/tex]

Final answer:

The upper specification limit for the plastic handle is 6.2 inches, and the lower specification limit is 5.8 inches, with these limits defining the acceptable range for the handle length.

Explanation:

The specification for a plastic handle is given as a length of 6.0 inches with a tolerance of ± 0.2 inches. This means the upper specification limit (USL) and the lower specification limit (LSL) are defined by adding and subtracting the tolerance to the target length respectively. The process standard deviation is 0.05 inches, but this does not affect the USL and LSL directly; it's a measure of the process variation.

The USL and LSL are calculated as follows:

These limits are the range within which the plastic handle lengths should fall according to the given specifications.

Step-by-step explanation:

I hope this is what you need

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Answer:

162 inches

Step-by-step explanation:

To get the answer you would have to know how many inches are a yard. The answer is 36. So you would have to multiply 4.5 by 36.

Answer:

Conversions :

1 ft = 12 in.

3 ft = 1 yard

Step-by-step explanation:

[tex]4.5 yards (\frac{3 ft}{1 yard} ) ( \frac{12 in.}{1 ft} ) = 162[/tex]

Answer:

y = -4x + 26

Step-by-step explanation:

y = mx + b    m: slope  -4   b: y intercept

pass (5 , 6)

b = y - mx = 6 - (-4) x5 = 6 + 20 = 26

equation: y = -4x + 26

Answer:

The 95% CI is (6.93% , 7.47%)

The 99% CI is (6.85% , 7.55%)

Step-by-step explanation:

We have to estimate two confidence intervals (95% and 99%) for the population mean 30-year fixed mortgage rate.

We know that the population standard deviation is 0.7%.

The sample mean is 7.2%. The sample size is n=26.

The z-score for a 95% CI is z=1.96 and for a 99% CI is z=2.58.

The margin of error for a 95% CI is

[tex]E=z\cdot \sigma/\sqrt{n}=1.96*0.7/\sqrt{26}=1.372/5.099=0.27[/tex]

Then, the upper and lower bounds are:

[tex]LL=\bar x-z\cdot\sigma/\sqrt{n}=7.2-0.27=6.93\\\\ UL=\bar x+z\cdot\sigma/\sqrt{n} =7.2+0.27=7.47[/tex]

Then, the 95% CI is

[tex]6.93\leq x\leq 7.47[/tex]

The margin of error for a 99% CI is

[tex]E=z\cdot \sigma/\sqrt{n}=2.58*0.7/\sqrt{26}=1.806/5.099=0.35[/tex]

Then, the upper and lower bounds are:

[tex]LL=\bar x-z\cdot\sigma/\sqrt{n}=7.2-0.35=6.85\\\\ UL=\bar x+z\cdot\sigma/\sqrt{n} =7.2+0.35=7.55[/tex]

Then, the 99% CI is

[tex]6.85\leq x\leq 7.55[/tex]

Answer:

(-7, 9]

Step-by-step explanation:

Assuming you want an answer in interval notation:

W is less than or equal to 9 >> [tex]w \leq 9[/tex]

W is greater than- 7 >> [tex]-7 < w[/tex]

Combine the two >> [tex]-7 < w \leq 9[/tex]

So in interval notation, (-7, 9]

Answer:

1/15

Step-by-step explanation:

Answer:

52 weeks

365 days

10 years

100 years

Step-by-step explanation:

Answer:

a) There is no significant evidence to conclude that there there is significant difference in the mean amount of paint per 1-gallon cans and 1 gallon.

b) The p-value obtained = 0.076727 > significance level (0.01), hence, we fail to reject the null hypothesis and conclude that there is no significant evidence to conclude that there there is significant difference in the mean amount of paint per 1-gallon cans and 1 gallon.

That is, the mean amount of paint per 1-gallon cans is not significantly different from 1 gallon.

c) The 99% confidence for the population mean amount of paint per 1-gallon cans is

(0.988, 0.999) in gallons.

d) The result of the 99% confidence interval does not agree with the result of the hypothesis testing performed in (a) because the right amount of paint in 1-gallon cans, 1 gallon, does not lie within this confidence interval obtained.

Step-by-step explanation:

a) This would be answered after solving part (b)

b) For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and is always about the absence of significant difference between two proportions being compared. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis takes the other side of the hypothesis; that there is indeed a significant difference between two proportions being compared. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, the null hypothesis is that there is no significant difference in the mean amount of paint per 1-gallon cans and 1 gallon. That is, the mean amount of paint per 1-gallon cans should be 1 gallon.

And the alternative hypothesis is that there is significant difference in the mean amount of paint per 1-gallon cans and 1 gallon. That is, the mean amount of paint per 1-gallon cans is not 1 gallon.

Mathematically,

The null hypothesis is

H₀: μ₀ = 1 gallon

The alternative hypothesis is

Hₐ: μ₀ ≠ 1 gallon

To do this test, we will use the z-distribution because we have information on the population standard deviation.

So, we compute the z-test statistic

z = (x - μ)/σₓ

x = the sample mean = 0.995 gallons

μ₀ = what the amount of paint should be; that is 1 gallon

σₓ = standard error = (σ/√n)

σ = standard deviation = 0.02 gallon

n = sample size = 50

σₓ = (0.02/√50) = 0.0028284271 = 0.00283 gallons.

z = (0.995 - 1) ÷ 0.00283

z = -1.77

checking the tables for the p-value of this z-statistic

p-value (for z = -1.77, at 0.01 significance level, with a two tailed condition) = 0.076727

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.01

p-value = 0.076727

0.076727 > 0.01

Hence,

p-value > significance level

So, we fail to reject the null hypothesis and conclude that there is no significant evidence to conclude that there there is significant difference in the mean amount of paint per 1-gallon cans and 1 gallon.

That is, the mean amount of paint per 1-gallon cans is not significantly different from 1 gallon.

c) To compute the 99% confidence interval for population mean amount of paint per 1-gallon paint cans.

Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample Mean) ± (Margin of error)

Sample Mean = 0.995 gallons

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value at 99% confidence interval is obtained from the z-tables because we have information on the population standard deviation.

Critical value = 2.58 (as obtained from the z-tables)

Standard error = σₓ = 0.00283 (already calculated in b)

99% Confidence Interval = (Sample Mean) ± [(Critical value) × (standard Error)]

CI = 0.995 ± (2.58 × 0.00283)

CI = 0.995 ± 0.0073014

99% CI = (0.9876986, 0.9993014)

99% Confidence interval = (0.988, 0.999) in gallons.

d) The result of the 99% confidence interval does not agree with the result of the hypothesis testing performed in (a) because the right amount of paint in 1-gallon cans, 1 gallon, does not lie within this confidence interval obtained.

Hope this Helps!!!

By calculating a z-value and comparing it to the critical value at alpha = 0.01, evidence can be determined. The p-value, as extreme as the calculated one assuming the null hypothesis is true, can be used to interpret the findings. Additionally, a 99% confidence interval estimate can be constructed to provide a range of values that is 99% confident in containing the true population mean amount of paint.

a. To determine whether the mean amount of paint contained in 1-gallon cans is different from 1.0 gallon, we can perform a hypothesis test. The null hypothesis (H0) is that the mean amount is 1.0 gallon, and the alternative hypothesis (Ha) is that the mean amount is different from 1.0 gallon. We can perform a z-test using the formula Z = (sample mean - population mean) / (standard deviation / sqrt(sample size)). In this case, the sample mean is 0.995 gallon, the population mean is 1.0 gallon, the standard deviation is 0.02 gallon, and the sample size is 50. By calculating the z-value, we can compare it to the critical value at alpha = 0.01 to determine whether there is evidence to reject the null hypothesis.

b. The p-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true. In this case, we can calculate the p-value using the standard normal distribution table or a calculator. If the p-value is less than the significance level (alpha = 0.01), we reject the null hypothesis. The interpretation of the p-value is that there is strong evidence to suggest that the mean amount of paint is different from 1.0 gallon.

c. To construct a 99% confidence interval estimate of the population mean amount of paint, we can use the formula CI = sample mean ± (z-score * (standard deviation / sqrt(sample size))). In this case, the z-score for a 99% confidence level is approximately 2.61. Plugging in the values, we can calculate the confidence interval, which gives us a range of values that we are 99% confident contains the true population mean amount of paint.

d. By comparing the results of (a) and (c), we can draw conclusions about whether the mean amount of paint is different from 1.0 gallon. If the null hypothesis is rejected in (a) and the 99% confidence interval in (c) does not include 1.0 gallon, then we can conclude that there is evidence to suggest that the mean amount is different from 1.0 gallon.

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Answer:

a) 0.760

b) 0.048

c) 0.192

Step-by-step explanation:

The step by step solution is attached as an image.

A) The probability of passing the test on the first or second try is 0.760.

That is he pass in the first trial or second trial.

(B) The probability of failing on the first 2 trials and passing on the third is 0.048.

That is the employee fail the first the trial and pass the third trial.

(C) The probability of failing on all 3 attempts is 0.192.

That is the employee fail all the three trial.

The probability of passing on the first or second try is 76%, the probability of failing the first 2 trials and passing on the third is 4.8%, and the probability of failing all 3 attempts is 19.2%.

This problem relates to the field of probability. Let's break it down.

For part A, the probability of passing on the first or second try is the sum of the probability of passing on the first try and the product of the probability of failing on the first try and passing on the second. This is calculated as 0.4 + (0.6*0.6) = 0.76 or 76%.

For part B, the probability of failing the first 2 trials and passing on the third is calculated by multiplying the probability of failing the first trial, failing the second, and passing the third: (0.6*0.4*0.2) = 0.048 or 4.8%.

For part C, the probability of failing all 3 attempts is equal to the product of the probability of failing each attempt: (0.6*0.4*0.8) = 0.192 or 19.2%.

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Answer:

And the F statistic calculated from the mean squares if [tex]F_{calc}[/tex]. And for this case we know that [tex] F_{calc}>F_{critical}[/tex]. So then we can reject the null hypothesis that all the means are equal at a significance level given [tex]\alpha[/tex]. And the best conclusion would be:

reject H0 since there is evidence all the means differ.

Step-by-step explanation:

Previous concepts

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".  

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"  

Solution to the problem

The hypothesis for this case are:

Null hypothesis: [tex]\mu_{A}=\mu_{B}=....=\mu_{k}[/tex]

Alternative hypothesis: Not all the means are equal [tex]\mu_{i}\neq \mu_{j}, i,j=A,B,...,k[/tex]

If we assume that we have [tex]p[/tex] groups and on each group from [tex]j=1,\dots,p[/tex] we have [tex]n_j[/tex] individuals on each group we can define the following formulas of variation:  

[tex]SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2 [/tex]  

[tex]SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2 [/tex]  

[tex]SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2 [/tex]  

And we have this property  

[tex]SST=SS_{between}+SS_{within}[/tex]  

And the F statistic calculated from the mean squares if [tex]F_{calc}[/tex]. And for this case we know that [tex] F_{calc}>F_{critical}[/tex]. So then we can reject the null hypothesis that all the means are equal at a significance level given [tex]\alpha[/tex]. And the best conclusion would be:

reject H0 since there is evidence all the means differ.

In a one-way ANOVA, if the computed F statistic is greater than the critical F value you may eject H0 since there is evidence all the means differ.

F test is a method used in statistics to determine which models best fits the population from which the sample is derived.

The formula for calculating  the F-test statistic = explained variance / unexplained variance

The null hypothesis usually states that the means are the means are the same while the alternative hypothesis states that the means are not the same.

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There are 12 valid arrangements for Sunhee to line up the four plastic shapes so that the circle is not next to the square.

In how many ways can Sunhee line up four plastic shapes (a square, a circle, and a pentagon) if the circle cannot be next to the square?

To solve this problem, we can count the total number of ways to arrange the shapes and then subtract the cases where the circle is next to the square.

1. Total ways to arrange the shapes:

Answer:

Therefore profit function is increasing on the interval (0,3200)

Step-by-step explanation:

The cost function of the manufacturer C(x) is given as:

[TeX]C(x)= 0.17x^{2}-0.00016x^{3}[/TeX]

The Revenue function is also given as:

[TeX]R(x)= 0.362x^{2}-0.0002x^{3}[/TeX]

Profit=Revenue-Cost

Therefore:

P(x)=R(x)-C(x)

[TeX]= 0.362x^{2}-0.0002x^{3}-[0.17x^{2}-0.00016x^{3}][/TeX]

[TeX]= 0.362x^{2}-0.0002x^{3}-0.17x^{2}+0.00016x^{3}[/TeX]

The Profit Function, [TeX]P(x)= 0.192x^{2}-0.00004x^{3}[/TeX]

To determine the point where the function is increasing, we take the derivative and examine it's critical points.

The derivative of the profit function is:

[TeX]P^{'}(x)= 0.384x-0.00012x^{2}[/TeX]

Set the derivative equal to zero.

[TeX]0.384x-0.00012x^{2}=0[/TeX]

[TeX]x(0.384x-0.00012x)=0[/TeX]

x=0 or [TeX]0.384-0.00012x=0[/TeX]

x=0 or [TeX]0.384=0.00012x[/TeX]

x=0 or x=3200

Now let's choose 2000 and 4000 as test points.

[TeX]P^{'}(2000)= 0.384(2000)-0.00012(2000)^{2}=288[/TeX]

[TeX]P^{'}(4000)= 0.384(4000)-0.00012(4000)^{2}=-384[/TeX]

Therefore profit function is increasing on the interval (0,3200)

Answer:

The is profit function is increasing on (0, 3200).

Step-by-step explanation:

Given

C(x) = 0.17x² - 0.00016x³

R(x) = 0.362x² - 0.0002x³

The profit function is given by

P(x) = R(x) - C(x)

P(x) = (0.362x² - 0.0002x³) - (0.17x² - 0.00016x³)

P(x) = 0.362x² - 0.0002x³ - 0.17x² + 0.00016x³

P(x) = 0.192x² - 0.00004x³

The derivative of the profit function is given by

P'(x) = 0.384x - 0.00012x²

Determine the critical number of P(x) to get interval where the profit function is increasing,

Set P'(x) = 0

0.384x - 0.00012x² = 0

x(0.384 - 0.00012x) = 0

x = 0 or 0.384 - 0.00012x = 0

0.384 - 0.00012x = 0

x = 0.384/0.00012 = 3200

Therefore the is profit function is increasing on (0, 3200)

Answer:

(-8-3)/(-8+10)= -11/2

y - 3 = -11/2(x+10)

y-3=-11/2x-55

y=-11/2x-52

Step-by-step explanation:

Answer:

7 jars per box

Step-by-step explanation:

He now has 41 jars. How many did he have before his teacher gave him 6?

Well, 41-6=35. He had 35 jars before his teacher gave him more.

It says there was an equal amount of jars in each box. There are 5 boxes. Divide the total amount of jars (35) by the amount of boxes to find out how many jars are in each box.

35 jars / 5 boxes = 7 jars / box

Answer:

  m = 57

Step-by-step explanation:

If we assume your equation is supposed to be ...

  512 = (m +7)^(3/2)

we can raise both sides to the 2/3 power to get ...

  512^(2/3) = m +7

  64 = m +7

  57 = m . . . . . . subtract 7

Answer: C

Step-by-step explanation:

Answer:The answer Is The Third One On The Right.

Step-by-step explanation:

Answer:

She has completed 2/3 of the poster

Explanation:

1/3 of the poster the first day

+

1/3 of the poster the next day

1/3 + 1/3 = 2/3

Answer:

54.98 degrees.

Step-by-step explanation:

In the diagram, the sides of the A-Frame are lengths AB and BC. The width of the cabin is length BC. We are to determine the measure of the angle at B, i.e. the angle between the two sides of the roof.

Using Cosine Rule:

[tex]b^2=a^2+c^2-2acCos B\\Cos B=\dfrac{b^2-a^2-c^2}{-2ac} \\B=arcCos(\dfrac{b^2-a^2-c^2}{-2ac} )\\a=26, b=24, c=26\\B=arcCos(\dfrac{24^2-26^2-26^2}{-2*26*26} )\\=arcCos 0.5739\\B=54.98^0[/tex]

The angle in between the two sides of the roof is 54.98 degrees.

To find the angle between the two sides of the roof of an A-frame cabin, we can use trigonometry and the Pythagorean theorem. The angle is approximately 22.33°.

To determine the angle between the two sides of the roof of an A-frame cabin, we can use trigonometry. Since the sides of the roof are both 26 feet long and the base of the cabin is 24 feet wide, we can consider the A-frame cabin as a right triangle. The roof line forms the hypotenuse of the triangle, and the sides of the triangle represent the rafters of the A-frame roof.

Using the Pythagorean theorem, we can find the height of the triangle (which is the distance from the base of the cabin to the point where the roof meets): h^2 = 26^2 - 12^2 = 676 - 144 = 532.

Taking the square root of both sides gives us h ≈ 23.07 feet.

Now, we can determine the angle by using trigonometric functions.

The sine function relates the opposite side (the height) to the hypotenuse (the roof line). So, sin(θ) = h / 26, where θ is the angle we want to find. Solving for θ gives us θ ≈ 22.33°.

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Answer:

the mean is 3

answer choice D

Step-by-step explanation:

60/20

Hence, the correct answer is 1/5

A random variable is a numerical valued variable on a defined sample space of an experiment with expressions such as X

probability distribution of random variable X is given by,

X        1        2        3        4        5

P(X)   1/5     1/5     1/5     1/5      1/5

mean of probability distribution = [tex]\frac{\sum{P(X)}}{5}[/tex]

                                                     = 1/5

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Answer:

[tex] P(1.28< X< 3.8) [/tex]

And we can use the z score formula to calculate how many deviations we are within the mean

[tex] z = \frac{X -\mu}{\sigma}[/tex]

And if we use this formula we got:

[tex] z = \frac{1.28-2.54}{0.42}= -3[/tex]

[tex] z = \frac{3.8-2.54}{0.42}= 3[/tex]

And using the empirical rule we know that within 3 deviation from the mean we have 99.7% of the values

Step-by-step explanation:

Previous concepts

The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)".

Let X the random variable who represent the grade point averages of undergraduate students.

From the problem we have the mean and the standard deviation for the random variable X. [tex]E(X)=2.54, Sd(X)=0.42[/tex]

So we can assume [tex]\mu=2.54 , \sigma=0.42[/tex]

On this case in order to check if the random variable X follows a normal distribution we can use the empirical rule that states the following:

• The probability of obtain values within one deviation from the mean is 0.68

• The probability of obtain values within two deviation's from the mean is 0.95

• The probability of obtain values within three deviation's from the mean is 0.997

For this case we want to find this probability:

[tex] P(1.28< X< 3.8) [/tex]

And we can use the z score formula to calculate how many deviations we are within the mean

[tex] z = \frac{X -\mu}{\sigma}[/tex]

And if we use this formula we got:

[tex] z = \frac{1.28-2.54}{0.42}= -3[/tex]

[tex] z = \frac{3.8-2.54}{0.42}= 3[/tex]

And using the empirical rule we know that within 3 deviation from the mean we have 99.7% of the values

Approximately 99.7 percent of the students have grade point averages between 1.28 and 3.8 according to the empirical rule.

The empirical rule states that approximately 68 percent of the data lies within one standard deviation of the mean, 95 percent lies within two standard deviations, and more than 99 percent lies within three standard deviations. In this case, the mean grade point average is 2.54 and the standard deviation is 0.42. To find the percentage of students with grade point averages between 1.28 and 3.8, we need to find the z-scores for both values and calculate the area under the curve between those z-scores.

First, we find the z-score for 1.28 using the formula: z = (x - µ) / σ = (1.28 - 2.54) / 0.42 = -3.0476. Then, we find the z-score for 3.8 using the same formula: z = (3.8 - 2.54) / 0.42 = 3.0476. Using a standard normal distribution table or a calculator, we can find the area between these two z-scores, which is approximately 99.7 percent.

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Answer:

im lost good luck

Step-by-step explanation:

Answer:

Josephine is 6 years old.

Step-by-step explanation:

6 * 5 = 30

12 * 3=  36

Josephine is currently 6 years old.

We are given two conditions about the ages of Josephine and her father.

Josephine’s father is 5 times as old as Josephine currently.

In 6 years, he will be only three times as old as she will be at that time.

Let's let 'J' represent Josephine's current age.

Then her father's current age would be 5J. In 6 years, Josephine will be J+6 and her father will be 5J+6.

According to the second condition, at that time her father's age will be three times Josephine's age.

So, we set up the equation 5J+6 = 3(J+6).

To find Josephine's current age, we solve the equation:

5J + 6 = 3J + 18

Subtract 3J from both sides:

2J + 6 = 18

Now subtract 6 from both sides:

2J = 12

And divide both sides by 2:

J = 6

Therefore, Josephine is currently 6 years old.

Answer:

(a) H1: μ < 530. Reject H1 if tcalc > –1.753

(b) t calc = –1.6. There is not enough evidence to reject the manufacturer’s claim.

Step-by-step explanation:

We are given that the manufacturer of an airport baggage scanning machine claims it can handle an average of 530 bags per hour.

A sample of 16 randomly chosen hours with a mean of 510 and a standard deviation of 50 is given.

Let [tex]\mu[/tex] = average bags an airport baggage scanning machine can handle

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 530 bags     {means that an airport baggage scanning machine can handle an average of more than or equal to 530 bags per hour}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 530 bags     {means that an airport baggage scanning machine can handle an average of less than 530 bags per hour}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

                         T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean = 510

             s = sample standard deviation = 50

            n = sample of hours = 16

So, test statistics  =  [tex]\frac{510-530}{\frac{50}{\sqrt{16} } }[/tex]  ~ [tex]t_1_5[/tex]

                              =  -1.60

The value of t test statistics is -1.60.

Now, at 0.05 significance level the t table gives critical value of -1.753 at 15 degree of freedom for left-tailed test. Since our test statistics is more than the critical values of t as -1.60 > -1.753, so we have insufficient evidence to reject our null hypothesis as it will not in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that an airport baggage scanning machine can handle an average of more than or equal to 530 bags per hour.

Answer:

a) The probability that exactly 41 of the murders were cleared is 0.0013

b) The probability that between 36 and 38 of the murders, inclusive, were cleared is 0.0809.

c) Yes, it would be unusual

Step-by-step explanation:

Let p=62% considered as the probability of having a commited that is cleared by arres or exceptional means. We assume that choosing each of the 50 commited is independent of each choose. Then, let X be the number of cleared. In this case, X is distributed as a binomial random variable. Recall that, in this case,

[tex] P(X=k) = \binom{50}{k} p^{k}(1-p)^{50-k}[/tex] for[tex]0\leq k \leq 50[/tex], with p=0.62

a) We have that

[tex] P(X=40) = \binom{50}{40} p^{40}(1-p)^{50-40} =0.001273487  [/tex]

b) We are asked for the following

[tex]P(36\leq X \leq 38) = P(X=36)+P(X=37)+P(X=38) = 0.080888936

[/tex] (The specific calculation is omitted.

c) We will check for the following probability [tex]P(X\leq 19)[/tex]

[tex]P(X\leq 19 ) = \sum_{k=0}^{19} P(X=k) = 0.000499222 [/tex]

Given that the probability of this event is really close to 0, it would be unusual if less than 19 murders are cleared.

The question deals with the application of binomial probability distribution in a real life situation involving crime investigation. The probability values for a certain range or exact number of cleared murders can be calculated by using the binomial probability formula. It would be statistically unusual for fewer than 19 murders to be cleared given a 62% clearance rate.

This question can be approached using the binomial distribution, where the number of successes in a sequence of n independent experiments (in this case, the number of murders being cleared) follows a binomial distribution.

a. The probability that exactly 41 of the murders were cleared can be found by calculating the binomial probability. This can be done by using the formula: P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k)). In this case, n=50 (number of trials/murders), k=41 (number of successes/murders cleared), and p=0.62 (probability of success/clearing a murder). You need to substitute these values into the formula and calculate the value.

b. Finding the probability that between 36 and 38 murders were cleared involves the same process, but you need to calculate for k=36, 37, and 38, and then add the results together to get the total probability.

c. If fewer than 19 of the murders were cleared, it would be statistically unusual considering the 62% clearance rate according to the survey. The reasoning being that, given a 62% probability, the expectation would be significantly higher.

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Answer: 152

Step-by-step explanation:

305 - 153 = 152

The height of the Statue of Liberty itself, without the pedestal, is 152 feet. This is found by subtracting the pedestal height (153 feet) from the total height (305 feet).

The student is asked to determine the height of the Statue of Liberty excluding its pedestal. Given that the total height of the Statue of Liberty including its pedestal is labeled as 305 feet, and the total height is 153 feet more than the height of the statue alone, we can set up the following equation to solve for the height of the statue (let's call it S):

S + 153 = 305

To find the height of the Statue of Liberty without the pedestal, we subtract 153 from both sides of the equation:
S = 305 - 153
S = 152

Therefore, the height of the Statue of Liberty itself is 152 feet.

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