The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 4639 4639 miles, with a standard deviation of 437 437 miles. If he is correct, what is the probability that the mean of a sample of 32 32 cars would differ from the population mean by less than 181 181 miles? Round your answer to four decimal places.

A personal trainer is interested in the typical physical activity of her clients. She asked a sample of her customers how many hours of exercise they get each week, and recorded the data below. Describe her findings using everything you've learned about measures of central tendency, measures of variability, and describe the shape of the distribution

х= 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8

1. A study released by the governor’s office stated that 60% of the state residents support a higher penalty for driving under influence. John thinks the number is low, so he decided to conduct his own survey. He interviews 100 people and find that 75% support a higher penalty for driving under influence. Identify the following: (1pt each)

- Sample:

- Population:

- Statistic:

- Parameter:

2. A bag contains 5 colored marbles, 3 red and 2 blue. You want to pick three marbles, one at a time from the bag. The sample space of this experiment is as followed:

S = {RRR, RRB, RBR, BRR, BBR, BRB, RBB}

We define the following event:

A – No pick is red

B – Exactly two picks are Red.

C – The second is Blue.

D – Exactly two Blue.

a. Is A and B disjoint or non-disjoint? (2pts)

b. Is C and D disjoint or non-disjoint? (2pts)

3. A carnival game has bag that contains four different colored balls. There are four blue balls, three red balls, two orange balls, and one purple ball. You pay $5 to reach in and grab one colored ball from the bag. If you pick a blue ball you win $10, if you pick a red ball you win $20, if you pick an orange ball you win $50, and if you pick a purple ball you win $100. What is your expected gain if you play this game? (3pts)

(1 point) Fireworks. Last summer, Survey USA published results of a survey stating that 301 of 538 randomly sampled Kansas residents planned to set off fireworks on July 4th. Round all results to 4 decimal places.

1. Calculate the point estimate for the proportion of Kansas residents that planned to set off fireworks on July 4th

2. Calculate the standard error for the point estimate you calculated in part 1.

3. Calculate the margin of error for a 99 % confidence interval for the proportion of Kansas residents that planned to set off fireworks on July 4th.

4. What are the lower and upper limits for the 99 % confidence interval. ( , )

5. Use the information from Survey USA poll to determine the sample size needed to construct a 99% confidence interval with a margin of error of no more than 2.7%. For consistency, use the reported sample proportion for the planning value of p* (rounded to 4 decimal places) and round your Z-value to 3 decimal places. Your answer should be an integer.

Explain why ρ is preferable to Cov(X,Y) in measuring the strength of relationship between X and Y

Use computer software packages, such as Excel, to solve this problem.

The Jacobs Chemical Company wants to estimate the mean time (minutes) required to mix a batch of material on machines produced by three different manufacturers. To limit the cost of testing, four batches of material were mixed on machines produced by each of the three manufacturers. The times needed to mix the material follow.

a. The following regression model can be used to analyze the data.

E(y) = B0+B1D1+B2D2

Show the values of the variables below. If your answer is zero enter “0”.

b. Show the estimated regression equation (to the nearest whole number and enter negative value as negative number).

y^=______+______D1 +_______D2

c. What null hypothesis should we test to determine if we should reject the assumption that the mean time to mix a batch is the same for all three manufacturers?

Select the number of the null hypothesis you would want to test.

- Select your answer -12345Item 6

d. What is the value of the test statistic in your hypothesis in part (c) (to 2 decimals)? Use Table 4 in Appendix B.

What is the -value?

- Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 8

What is your conclusion?

- Select your answer -Conclude that the mean time is not the same for all three manufacturersConclude that the mean time is same for all three manufacturersItem 9

For a normal population with known variance σ², what value of z_α/2 in the Equation below gives a 98% CI?

            x-zα/2σn≤μ≤x+zα/2σn

Binomial distributions are approximately normal when the number of trials is large, and the probaility of success is not near zero or one. A player flips an unbiased coin 1,296 times.

a. What is the probability of the coin landing on heads between 612 and 684 times?

According to a​ survey, 63​% of murders committed last year were cleared by arrest or exceptional means. Fifty murders committed last year are randomly​ selected, and the number cleared by arrest or exceptional means is recorded. When technology is​ used, use the Tech Help button for further assistance.

​(a) Find the probability that exactly 40 of the murders were cleared. ​

(b) Find the probability that between 35 and 37 of the​ murders, inclusive, were cleared.

​(c) Would it be unusual if fewer than 18 of the murders were​ cleared? Why or why​ not?

In a Union-Management negotiation, the following are the annual percentages of wage increases for Union for various combinations of union and management strategies:

Management

M1 M2 M3

U1 1 3 3

U2 4 2 2

Union U3 3 2 3

U4 3 4 1

U5 2 1 2

9a. (5 points) After eliminating all possible dominated strategies, list the Union payoff matrices for the 4 subgames that are developed by taking 3 of the 4 Union strategies to match the 3 Management strategies.

9b. (5 points) Find the best strategy and value of the game for Union with the following payoff matrix for one of the subgames:

Management

M1 M2 M3

U2 4 2 2

Union U3 3 2 3

U4 3 4 1

9c. (10 points) We have solved in class the best strategy and value of the game for Union with the following payoff matrix for one of the subgames:

Management

M1 M2 M3

U1 1 3 3

Union U3 3 2 3

U4 3 4 1

Let q1, q2, and q3 be the respective probabilities for Management to play strategies M1, M2, and M3. Then use the same Principle of Maximin as in deraiving the best mixed strategy for Union to find the best strategy and value of the game for Management. Specifically,

9c1 (5 points) show the three independent linear equations for q1, q2, and q3.

9c2 (5 points) Show the correct solution for these 3 probabilities from these 3 independent linear equations.

assume that in 2018 the mean mathematics sat score was 536 and the standard deviation was 115. a sample of 68 scores is chosen. a) what is the sampling distribution of *? b) what is the probability the sample mean score is less than 510? c) what is the probability the sample mean score is between 485 and 525? d) what is the probability the sample mean score is greater than 480? e) would it be unusual for the sample mean to be greater than 575? show work to prove your answer.

1. What is the nature of heteroscedasticity?
2. What are the consequences of heteroscedasticity?
3. How is heteroscedasticity detected? (Focus on the White-test)
4. What are the remedial measures? (Focus on Weighted-Least-Squares)

The transmission delay between two linked wireless devices is a normal variable with a mean of 60 milliseconds and a standard deviation of 5 milliseconds.

a. What is the probability that a transmission delay is more than 65 milliseconds?

b. What is the probability that a transmission delay is between 55 and 70 milliseconds?

c. What is the probability that a transmission delay is more than 45 milliseconds?

d. Agents for the NSA notice a transmission delay greater than 80 milliseconds. Is this a rare enough event to warrant suspicion that enemy agents are dampening the signal strength?

Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical values of r given the number of pairs of data n and the significance level .

n = 14,  = 0.05

A; r = 0.532

B; r = ±0.532

C; r = 0.553

D; r = ±0.661

A administrator wants to know what is the average starting salary, μ, for students graduating from her college. She is able to obtain data for 100 randomly selected students. For these 100 students, the average is $70,000, and the SD is $10,000. What is a 99% confidence interval for μ?