statistics

1. It is known from past experience, that 8%(0.08) of the items produced by a machine are defective. In a new study, a random sample of 175 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 11%(0.11)?

C. What is the probability that the sample proportion of defects is less than 4%(0.04)?

D. How large would the sample proportion have to be to be in the top 5% of the distribution?

2. A recent survey of 50 managers who were laid off during the recent recession revealed it took a mean of 26 weeks for them to find another position. The standard deviation of the sample was 6.2 weeks. Construct and explain a 98% confidence interval estimate of the population mean time for managers to find another position.

3. Pharmaceutical companies promote their prescription drugs using television advertising. In a survey of 600 randomly selected television viewers, 100 indicated that they asked their physician about using a prescription drug they saw on TV. Compute and explain a 90% confidence interval estimate of the population proportion.

4. Management of a large manufacturing company is considering adopting a bonus system to increase production. Past records indicate that production is normally distributed with a mean of 2500 units per week and a standard deviation of 75 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. In the United States, the mean age of men when they marry for the first time follows a normal distribution with a mean of 29 years. The standard deviation of this population is 3.5 years. A random sample of 40 mean will be used for a new study.

A. What is the Shape, Mean (expected value) and Standard Deviation of the Sampling Distribution of the sample mean for samples of size 40?

B. What is the probability that the sample mean will be larger than 30 years?

C. What is the probability that the sample mean will be between 27.5 years and 30.5 years?

6. A research firm sampled 65 randomly selected individuals to determine the mean amount spent on coffee in one week. The sample showed a mean of $20. The population is assumed to be normally distributed with a population standard deviation of $5.50. Construct and explain a 99% confidence interval estimate of the population mean amount spent on coffee in one week.

7. A recent study reported that Americans spend an average of 270 minutes per day watching TV. Assume the distribution of minutes per day watching TV follows a normal distribution with a standard deviation of 23 minutes.

A. What is the probability that a randomly selected American watches more than 305 minutes per day?

B. What is the probability that a randomly selected American watches less than 250 minutes per day?

C. What is the probability that a randomly selected American watches between 260 minutes and 280 minutes per day?

D. A "binge watcher" is someone in the upper 10% of the distribution. How many minutes per day must a "binge watcher" watch?

8. You want to estimate the mean family income in a rural area of the state. How many families should be sampled to estimate the population mean income at 95% confidence and a margin of error of $100? Assume that the population standard deviation of family income is $500.