A bus travels between two cities A and B that are 100 miles apart.Two service stations are located at mile 30 and mile 70, as well as in the cities themselves. The bus breaks down on the road. Assuming the place of breakdown is uniformly distributed between the cities, what is the probability that it is no more than 10 miles to the nearest service station? What is the expectation of the distance to the nearest service station?

The researchers classified gas turbines into three categories: traditional, advanced, and aeroderivative. Mean heat rate and standard deviation of heat rate for

• Advanced are 9764 and 639
• Aeroderiv are 12312 and 2652
• Traditional are 11544 and 1279

Is there sufficient evidence of a difference between the mean heat rates of traditional turbines and aeroderivative turbines at  alpha =0.05 ? Show all the work

Briefly describe the product-process matrix and the customer-contact matrix for service processes。

In a clinical trial, 401,974 adults were randomly assigned to two groups. The treatment group consisted of 201,229 adults given a vaccine and the other 200,745 adults were given a placebo. Among the adults in the treatment group, 33 adults developed the disease and among the placebo group, 115 adults developed the disease. The doctors' claim that the rate for the group receiving the vaccine is less than the group receiving the placebo. Answer the following questions:

a. If w idenitfy the symbolic null and alternative hypothesis.

b. If the P-value for this test is reported as "less than 0.001", what is your decision? What would you conclude about the original claim?

c. Assume that we want to use a 0.05 significance level to test the claim that p1 < p2. If we want to test that claim by using a confidence interval, what confidence level should we use?

d. If we test the original claim, we get the confidence interval -0.000508 < p1 - p2 < −0.000309 , what does this confidence interval suggest about the claim? e. In general, when dealing with inferences for two population proportions, which two of the following are equivalent: Confidence Interval method; P-value method; Critical Value method? Explain.

Jobs and productivity! How do retail stores rate? One way to answer this question is to examine annual profits per employee. The following data give annual profits per employee (in units of 1 thousand dollars per employee) for companies in retail sales. Assume σ ≈ 3.7 thousand dollars.

(a) Use a calculator or appropriate computer software to find x for the preceding data. (Round your answer to two decimal places.)
thousand dollars per employee

(b) Let us say that the preceding data are representative of the entire sector of retail sales companies. Find an 80% confidence interval for μ, the average annual profit per employee for retail sales. (Round your answers to two decimal places.)

c) Find an 95% confidence interval for μ, the average annual profit per employee for retail sales. (Round your answers to two decimal places.)

The following data represent petal lengths (in cm) for independent random samples of two species of Iris.

Petal length (in cm) of Iris virginica: x₁; n₁ = 35

Petal length (in cm) of Iris setosa: x₂; n₂ = 38

(a) Use a calculator with mean and standard deviation keys to calculate x₁, s₁, x₂, and s₂. (Round your answers to two decimal places.)

(b) Let μ₁ be the population mean for x₁ and let μ₂ be the population mean for x₂. Find a 99% confidence interval for μ₁ − μ₂. (Round your answers to two decimal places.)

David E. Brown is an expert in wildlife conservation. In his book The Wolf in the Southwest: The Making of an Endangered Species (University of Arizona Press), he records the following weights of adult grey wolves from two regions in Old Mexico.

Chihuahua region: x₁ variable in pounds

Durango region: x₂ variable in pounds

(a) Use a calculator with mean and standard deviation keys to calculate x₁, s₁, x₂, and s₂. (Use 2 decimal places.)

(b) Let μ₁ be the mean weight of the population of all grey wolves in the Chihuahua region. Let μ₂ be the mean weight of the population of all grey wolves in the Durango region. Find a 99% confidence interval for μ₁ – μ₂. (Use 2 decimal places.)

To evaluate the performance of inspectors in a new company, a quality manager had a sample of 12 novice inspectors evaluate 200 finished products. The same 200 items were evaluated by 12 experienced inspectors. SD of error for the novice inspectors was 8.64 and for the experiences inspectors was 5.74.

Was the variance in inspection errors lower for experienced inspectors than for novice inspectors? Conduct a hypothesis testing at  alpha = 0.05 and show all the work.

The number of men and women among professors in Math, Physics, Chemistry, Linguistics, and English departments from a SRS of small colleges were counted, and the results are shown in the table below.

Test the claim that the gender of a professor is independent of the department. Use the significance level α=0.01

(a) The test statistic is χ^2=

Suppose 130 geology students measure the mass of an ore sample. Due to human error and limitations in the reliability of the​ balance, not all the readings are equal. The results are found to closely approximate a normal​ curve, with mean

82g and standard deviation

1g. Use the symmetry of the normal curve and the empirical rule as needed to estimate the number of students reporting readings between 79

g and 85g.

The length of time to complete a door assembly on an automobile factory assembly line is normally distributed with mean μ=7.3 minutes and standard deviation σ=2 minutes. Samples of size 70 are taken. What is the mean value for the sampling distribution of the sample means?

The length of time to complete a door assembly on an automobile factory assembly line is normally distributed with mean μ=7.2 minutes and standard deviation σ=2.4 minutes. Samples of size 100 are taken. To the nearest thousandth of a minute, what is the standard deviation of the sampling distribution of the sample means?

Find P(46≤x¯≤53) for a random sample of size 35 with a mean of 51 and a standard deviation of 12.   (Round your answer to four decimal places.)

At a gymnastics meet, three judges evaluate the balance beam performances of five gymnasts. The judges use a scale of 1 to 10, where 10 is a perfect score. A statistician wants to examine the objectivity and consistency of the judges. Assume scores are normally distributed. (You may find it useful to reference the q table.)

a-1. Construct an ANOVA table. (Round intermediate calculations to at least 4 decimal places. Round "SS", "MS", "p-value" to 4 decimal places and "F" to 3 decimal places.)

a-2. If average scores differ by gymnast, use Tukey’s HSD method at the 5% significance level to determine which gymnasts’ performances differ. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round your answers to 2 decimal places.)

1. Nobel is a serial gambler and regularly plays several rounds of a gamble in which he wins $10,000 if the head comes on top twice when a fair coin is flipped twice and loses $5,000 for any other outcome from the two flips of the coin. In other words, the outcome of the gamble is determined by flipping a coin twice on each round of the gamble and Nobel wins only if head comes on top on both flips of the coin and loses if any other outcome occurs. Nobel is considering to play 10 rounds of such a gamble next week hoping that he will win back the $20,000 he lost in a similar gamble last week. If we let X represent the number of wins for Nobel out of the next 10 rounds of the gamble, X can be assumed to have a binomial probability distribution. Please answer the following questions based on the information given above.

a. Please calculate the probability of success for Nobel on each round of the gamble. Show how you arrived at your answer.

b. What is the probability that Nobel will win none of the 10 rounds of the gamble?  

c. What is the probability that Nobel will lose more than 5 of the 10 rounds of the gamble?   

d. What is the probability that Nobel will win at least 8 out of the 10 rounds of the gamble?   

e. What is the probability that Nobel will lose less than 4 of the 10 rounds of the gamble?   

f. What is the probability that Nobel will lose no more than 7 out of the 10 rounds of the gamble? g. How much money is Nobel expected to win in the 10 rounds of the gamble? How much money is he expected to lose? Given your results, do you think Nobel is playing a smart gamble? Please show how you arrived at your results and explain your final answer.

h. Calculate and interpret the standard deviation for the number of wins for Nobel in the next 10 rounds of the gamble. Show your work.

2. Vehicles arrive at a toll bridge at an average rate of 180 an hour. Only one toll booth is currently open and can process arrivals (collect tolls) at a mean rate of 22 seconds per vehicle.

A. How many vehicles should be expected at the toll bridge in a 10-minute period? Please show how you arrived at your answer.

B. Define X to be the number of vehicles arriving at the toll bridge in a 10-minute period and assume that X has a Poisson Probability distribution. Please calculate the probability that 25 vehicles will arrive at the toll bridge in a 10-minute period.

C. Please calculate the probability of at least 20 vehicles arriving at the bridge within 10-minute period.                                                                  

D. Please calculate the probability of less than 28 vehicles arriving at the bridge within 10-minute period.

E. Please calculate the probability that no vehicle will arrive at the bridge within a 10-minute period.

F. Please calculate the probability of more than 35 vehicles arriving at the bridge within a 10-minute period. Show your work.   

G. Please calculate the probability of at most 22 vehicles arriving at the bridge within a 10-minute period. Show your work.

G. Calculate and interpret the standard deviation of X.   

I. For what purpose can the kind of information you have calculated above be used? If the state department of transportation wants to reduce the average wait time for the drivers to less than 25 seconds at the toll bridge, do you think they should open another toll booth at the bridge? Please explain.             

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

The National Council of Small Businesses is interested in the proportion of small businesses that declared Chapter 11 bankruptcy last year. Since there are so many small businesses, the National Council intends to estimate the proportion from a random sample. Let p be the proportion of small businesses that declared Chapter 11 bankruptcy last year.

(a) If no preliminary sample is taken to estimate p, how large a sample is necessary to be 99% sure that a point estimate p̂ will be within a distance of 0.09from p? (Round your answer up to the nearest whole number.)
small businesses

(b) In a preliminary random sample of 30 small businesses, it was found that ten had declared Chapter 11 bankruptcy. How many more small businesses should be included in the sample to be 99% sure that a point estimate p̂ will be within a distance of 0.090 from p? (Round your answer up to the nearest whole number.)
more small businesses

Use R to do each of the following. Use R code instructions that are as general as possible, and also as efficient as possible. Use the Quick-R website for help on finding commands. 1. The following is a random sample of CT scores selected from 32 Miami students. 28, 27, 29, 27, 29, 31, 32, 30, 34, 30, 27, 25, 30, 32, 35, 32 23, 26, 27, 33, 33, 33, 31, 25, 28, 34, 30, 33, 28, 26, 30, 28 (a) Find the mean and standard deviation of this sample. Give the interpretation of the mean in the context. (b) Find the five numbers summary and provide the interpretation of the sample median in the context. (c) Draw the histogram of the data. What can you say about the distribution of the data. (d) Draw the Boxplot of the data. Is there any potential outlier? 2. The weekly amount spent for maintenance and repairs in a certain company has an approximately normal distribution, with a mean of $600 and a standard deviation of $40. If $700 is budgeted to cover repairs for next week, (a) what is the probability that the actual costs will exceed the budgeted amount? (b) how much should be budgeted weekly for maintenance and repairs to ensure that the probability that the budgeted amount will be exceeded in any given week is only 0.1?