1.

For a normally distributed set of scores with a standard deviation of 24, you would like to take a sample such that the standard error is 4 points. What is the sample size you need?

2.

The height of American men is normally distributed with a mean of 5'10" (or, in inches, 70") and standard deviation of 3".

a. If you studied a sample of 25 American men, what would you expect their mean height to be?

b. On average, how much would you expect the mean height of a sample of 25 American men to differ from the population mean of 70 inches?

3.

Suppose that the life of AA batteries follows a normal distribution with a mean of 90 hours and a standard deviation of 4. You just bought a pack of 16 AA batteries.

a. What is the probability that your pack of batteries would last an average of at least 88 hours?

b. What is the probability that your pack of batteries would last an average of 91 to 92 hours?

4.

Researchers believe that scores on a measure of attention span (defined as the amount of time spent attending to a task) is normally distributed. Two separate research studies attempted to estimate the true population mean using a sample. The first study used a sample of 81 individuals, while the second study had a sample of 36.

a. Which study would likely obtain a sample mean that is closer to the true population mean? Explain your answer.

b. CHALLENGE QUESTION (OPTIONAL): Suppose that the true population mean on this measure is 21 minutes with a standard deviation of 9. Which sample has a lower probability of obtaining a sample mean of 24 or higher? Explain your answer.