1. It is known from past experience, that 10%(0.10) of the items produced by a machine are defective. In a new study, a random sample of 75 items will be selected and checked for defects.

A. What is the Mean (expected value), Standard Deviation, and Shape of the sampling distribution of the sample proportion for this study?

B. What is the probability that the sample proportion of defects is more than 13%(0.13)?

C. What is the probability that the sample proportion of defects is less than 5%(0.05)?

2. In order to estimate the Mean weight of carry-on luggage, an airline selected and weighed, a random sample of 25 pieces of carry-on luggage. The sample mean was 32 pounds with a sample standard deviation of 9 pounds. Compute and explain a 90% confidence interval estimate of the population mean weight of all carry-on luggage.

3. In a survey, 600 consumers were asked whether they would like to purchase a domestic or a foreign made automobile. 340 said that they preferred to purchase a domestic made automobile. Construct and explain a 95% confidence interval estimate for the proportion of all consumers who prefer domestic automobiles.

4. Management of a large manufacturingcompany is considering adopting a bonus system to increase production. Past records indicate that production is normally distributed with a mean of 4000 units per week and a standard deviation of 80 units per week. If the bonus is to be paid when production reaches the top 5% of production, how many units must be produced in a week for the bonus to be paid?

5. The Mean life expectancy of Men in the U.S. is 78 years , with a population standard deviation of 7 years. A new study is using a random sample of 64 men to study life expectancy.

A. What is the Shape, Mean (expected value) and standard deviation of the sampling distribution of the sample mean for this study?

B. What is the probability that the sample mean will be larger than 80 years?

C. What is the probability that the sample mean will be less than 80 years?

6. A new study of working mothers used a random sample of 75 children with working mothers and it showed that the children were absent from school an average of 6 days per term. Assume that the population standard deviation of children with working mothers were absent from school is 1.5 days per term. Compute and explain a 95% confidence interval estimate of the mean number of days all children with working mothers were absent from school.

7. Scores on a recent national Mathematics exam were normally distributed with a mean of 82 and a standard deviation of 7.

A. What is the probability that a randomly selected exam score is less than 70

B. What is the probability that a randomly selected exam score is greater than 90?

C. If the top 2.5% of test scores receive Merit awards, what is the lowest score necessary to receive a merit award?

8. If the standard deviation of the lifetime of washing machines is assumed to be 500 hours of use, how large of a sample must be taken to be 90% confident that an estimate of the population Mean hours of use will have a margin of error of not more than 50 hours?