Review 1. Calculate the mean for the discrete probability distribution shown here.

X 2 4 5 10

P(X) .2 .2 .3 .2

2. It has been stated that 20% of the general population donate their time and energy to working on community projects. Suppose 20 people have been randomly sampled from a community and asked if they donated their time and energy to community projects. Let x be the number of them that do donate their time and energy to community projects. Find the probability that more than seven of the 20 do donate their time and energy to community projects.

3. A firm believes the internal rate of return for its proposed investment can best be described by a normal distribution with mean 20% and standard deviation 3%. What is the probability that the internal rate of return for the investment will be at least 15.5%?

4. The board of examiners that administers the real estate broker's examination in a certain state found that the mean score on the test was 435 and the standard deviation was 72. If the board wants to set the passing score so that only the best 10% of all applicants pass, what is the passing score? Assume that the scores are normally distributed.

5. The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 8,300 miles. If the manufacturer guarantees the tread life of the tires for the first 50,000 miles, what proportion of the tires will need to be replaced under warranty?

6. The amount of money collected by the snack bar at a large university has been recorded daily for the past five years. Records indicate that the mean daily amount collected is $2,500 and the standard deviation is $400. The distribution is skewed to the right due to several high volume days (football game days). Suppose that 100 days were randomly selected from the five years and the average amount collected from those days was recorded. Describe the sampling distribution of the sample mean? 7. The scores shot by professional golfers on a particular course have a mean of 70 strokes and a standard deviation of three strokes. Suppose 40 professional golfers played the course today. Find the approximate probability that the average score for the 40 golfers was below 72.

8. Electric power plants that use water for cooling their condensers sometimes discharge heated water into rivers, lakes, or oceans. It is known that water heated above certain temperatures has a detrimental effect on the plant and animal life in the water. Suppose it is known that the increased temperature of the heated water discharged by a certain power plant on any given day has a distribution with a mean of 50C and a standard deviation of 50C. Suppose a sample of n = 50 days was collected. What is the approximate probability that the average increase in temperature of the discharged water exceeds 60C.

9. The length of time to complete a door assembly on an automobile factory assembly line is distributed with mean µ = 7.0 minutes and standard deviation  = 5.0 minutes. What is the probability that the mean assembly time for a random sample of 100 doors will be: o At least 6 minutes

o 8 minutes or less

o Between 6.0 and 6.5 minutes

o Between 4.5 and 8 minutes

10. A physician wanted to estimate the mean length of time that a patient had to wait to see him after arriving at the office. A random sample of 36 patients showed a mean waiting time of 23.4 minutes and a standard deviation of 7.2 minutes. Find a 96% confidence interval for .

11. Barbara wanted to estimate the mean connection time to the Internet. She connected 25 times with a mean of 42 and a standard deviation of 5.2 minutes. Find a 90% confidence interval for .

12. A sample of 121 calls to the 900 number you operate has a mean duration of 16.6 minutes and a standard deviation of 3.63 minutes. You offer a discount, which will be discontinued unless the mean call duration exceeds 18 minutes. At the 90 percent level of confidence, what is your decision? Based on this study, do you think the service discount should be discontinued?

13. To estimate the proportion p of passengers who had purchased tickets for more than $400 over a year's time, an airline official obtained a random sample of 75. The number of those purchasing tickets for more than $400 was 45. (a) What is a point estimate for p?

(b) Find a 90% confidence interval for p.

(c) How many passengers are required in the sample to reduce in half the sampling error within which we need to estimate the proportion of passengers who had purchased tickets for more than $400 over a year's time?

14. A city council commissioned a statistician to estimate the proportion p of voters in favor of a proposal to build a new library. The statistician obtained a random sample of 200 voters, with 112 indicating approval of the proposal. What is a point estimate for p? Find a 99% confidence interval for p.

15. A coin is tossed 1000 times and 540 heads appear. Find a 95% confidence interval for the true proportion of heads.

16. A marketing research company is estimating the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 90% confidence interval was calculated to be Give a practical interpretation of the confidence interval.

17. If you wish to estimate a population mean within 0.2 using a 98% confidence interval and you know from prior sampling of sample size n = 500 that s is equal to 5.0. How many more observations would you have to include in your sample?

18. Allen is an appliance salesman who works on commission. A random sample of 49 days showed that the sample standard deviation for value of sales was S = $202. How many days must be included in the sample to be 99% sure the population mean μ is within $45 of the sample mean X-bar?

19. A nurse at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she desires to be 90% confident that the true mean is within 2 ounces of the sample mean? The standard deviation of the birth weights is known to be 10 ounces.