Use R to answer the following question. Copy and paste the code and answer from R into your paper.

On the average,five cars arrive at a particular car wash every hour. Let X count the number of cars that arrive from 10 AM to 11 AM. Then X ∼pois(lambda = 5). Also, μ = σ2 = 5.
 What is the probability that no car arrives during this period?
 Suppose the car wash above is in operation from 8AM to 6PM, and we let Y be the number of customers that appear in this period. Since this period covers a total of 10 hours. What is the probability that there are between 48 and 50 customers, inclusive?

There are ten volunteers, from whom we must choose three people for the committee. Three of the volunteers are women. Define ?? to be the number of women in the group of three that are chosen for the committee.

a. How many ways can you choose three people out of 10?

b. Find the exact probability, ??(?? = 2).

c. Find the exact probability, ??(?? ≥ 2).

Use the given categorical data to construct the relative frequency distribution.

Natural births randomly selected from four hospitals in a highly populated region occurred on the days of the week (in the order of Monday through Sunday) with the frequencies 52, 64, 72, 55, 57, 45, 55. Does it appear that such births occur on the days of the week with equal frequency?

Construct the relative frequency distribution.

Day              Relative frequency

Monday               ___%

Tuesday            ___%

Wednesday       ___%

Thursday           ____%

Friday                ___%

Saturday             ___%

Sunday               ____%

(Type integers or decimals. Round to two decimal places as needed.)

Let the frequencies be substantially different if any frequency is at least twice any other frequency, Does it appear that these births occur on the days of the week with equal frequency?

A. Yes, it appears that births occur on the days of the week with frequencies that are about the same.

B. No, it appears that births occur on the days of the week with frequencies that are substantially different.

C. Yes, it appears that births occur on the days of the week with frequencies that are exactly the same.

D. It is impossible to determine with the given information.

A random sample is drawn from a normally distributed population with mean μ = 23 and standard deviation σ = 2.6. [You may find it useful to reference the z table.]

a. Are the sampling distribution of the sample mean with n = 31 and n = 62 normally distributed?

• Yes, both the sample means will have a normal distribution.

• No, both the sample means will not have a normal distribution.

• No, only the sample mean with n = 31 will have a normal distribution.

• No, only the sample mean with n = 62 will have a normal distribution.

b. Calculate the probabilities that the sample mean is less than 23.7 for both sample sizes. (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

According to the National Automobile Dealers Assoc., 75% of U.S. car dealers' profits comes from repairs and parts sold. However, many of the dealerships' service departments aren't open evenings or weekends. The percentage of dealerships opened during the evenings and weekends are as follows:

a. Are the listed times mutually exclusive?

b. What is the probability that a car dealership selected at random is not open in the evenings or on the weekends?

c. Suppose two car dealerships, say, Dealership A and Dealership B, are each selected at random from car dealerships in the United States. What is the probability that both are open in the evenings but not on the weekends, or that both are open on the weekends but not in the evenings?

d. For the two dealerships in part c, what is the probability that Dealership A is open in the evenings but not on the weekends, and Dealership B is open on the weekends but not in the evenings?

e. For the two dealerships in part c, what is the probability that one of them is open in the evenings but not on the weekends, and that the other is open on the weekends but not in the evenings?

. A highway department executive claims that the number of fatal accidents which occur in her state does not vary from month to month. The results of a study of 170 fatal accidents were recorded. Is there enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month?

Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Fatal Accidents :

11 19 24 16 11 7 7 17 9 19 18 12

State the null and alternative hypothesis.

What does the null hypothesis indicate about the proportions of fatal accidents during each month?

State the null and alternative hypothesis in terms of the expected proportions for each category.

Find the value of the test statistic. Round your answer to three decimal places.

Find the degrees of freedom associated with the test statistic for this problem.

Find the critical value of the test at the 0.01 level of significance. Round your answer to three decimal places.

Make the decision to reject or fail to reject the null hypothesis at the 0.01 level of significance.

State the conclusion of the hypothesis test at the 0.01 level of significance.

Post a description of the types of probability and nonprobability sampling you selected. Then describe two strengths and two weaknesses of each type of sampling. Finally, identify two ethical considerations that may factor into selecting a sampling method and explain how you might address these considerations.

Using the data below, suppose we focus on the proportions of patients who show improvement. Is there a statistically significant difference in the proportions of patients who show improvement between treatments 1 and 2. Run the test at a 5% level of significance.

Resistance training is a popular form of conditioning aimed at enhancing sports performance and is widely used among high school, college, and professional athletes, although its use for younger athletes is controversial. Researchers obtained a random sample of 3933 patients between the ages of 8 and 30 who were admitted to U. S. emergency rooms with injuries classified by the Consumer Product Safety Commission code "weight-lifting." These injuries were further classified as " accidental" if caused by dropped weight or improper equipment use. Of the 3933 weight-lifting injuries, 1648 were classified as accidental.

What is a 98% confidence interval for the proportion of weight-lifting injuries in this age group that were accidental?

The 98% confidence interval (±±0.001) is from  to

Erin O'Brien, Director of Consumer Credit with Auckland First Bank (AFB), has implemented a 'fast feedback' to keep her informed of the default rate on personal loans at AFB member banks. On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. The 90% confidence interval for the population proportion is _________. Select one: a. 0.046 to 0.074 b. 0.039 to 0.081 c. 0.043 to 0.077 d. 0.028 to 0.060

Sixty eight cities provided information on vacancy rates (in percent) in local apartments in the following frequency distribution. The sample mean and the sample standard deviation are 9% and 3.2%, respectively. (You may find it useful to reference the appropriate table: chi-square table or F table)

Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

Make Excel do all calculations, using cell addresses. Don’t type numbers in your formulas.

Report the answers to the questions in your worksheet using the appropriate symbols (µ σ) and notation p(x>=5), p(X<3) etc...

            Use Insert/Symbol to find mu and sigma for mean and std dev.

1. An auditor for Health Maintenance Services of Georgia reports 30 percent of policyholders 55 years or older submit a claim during the year. Twelve policyholders are randomly selected for company records.

a. What type of distribution is this likely to be?

b. What is the expected number (mean) of the distribution?

c. What is the standard deviation of the distribution?

Use the tables in your text to answer the following questions

d. What is the probability that exactly 6 of the 12 policyholders have filed a claim?

e. What is the probability that more than 6 of the 12 policyholders have filed a claim?

f. What is the probability that 6 or fewer of the 12 policyholders have filed a claim?

g. What is the probability that at least 6 of the 12 policyholders have filed a claim?

Use the BINOMDIST function to answer the following questions

h. What is the probability that exactly 8 of the 12 policyholders have filed a claim?

i. What is the probability that more than 8 of the 12 policyholders have filed a claim?

j. What is the probability that 8 or fewer of the 12 policyholders have filed a claim?

k. What is the probability that at least 8 of the 12 policyholders have filed a claim?

A electronics manufacturer has developed a new type of remote control button that is designed to operate longer before failing to work consistently. A random sample of 20 of the new buttons is selected and each is tested in continuous operation until it fails to work consistently. The resulting lifetimes are found to have a sample mean of ?¯ = 1260.4 hours and a sample standard deviation of s = 116.1. Independent tests reveal that the mean lifetime of the best remote control button on the market is 1200 hours. Conduct a hypothesis test to determine if the new button's mean lifetime exceeds 1200 hours. Round all calculated answers to four decimal places.

1. The null hypothesis is ?0:?=1200. What is the alternate hypothesis? A. ??:?=1260.4 B. ??:?>1200 C. ??:?≠1200 D. ??:?<1200 E. ??:?>1260.4

2. Which of the following conditions must be met to perform this hypothesis test? Select all the correct answers. A. The number of remote control buttons tested must be normally distributed. B. We must be able to expect that at least 5 buttons will fail to work consistently. C. The sample must be large enough so that at least 10 buttons fail and 10 succeed. D. The observations must be independent. E. The lifetime of remote control buttons must be normally distributed.

3. Calculate the test statistic =

4. Calculate the p-value

5. Calculate the effect size, Cohen's d, for this test. ?̂ =

6. The results of this test indicate we have a... A. moderate to large B. large C. small D. small to moderate effect size, and... A. some evidence B. little evidence C. very strong evidence D. extremely strong evidence E. strong evidence that the null m odel is not compatible with our observed result.