Problem 1

A random sample of 16 adult males is about to get into an elevator which has a weight capacity of 2900 lbs. The adult male weight follows the normal distribution with a mean of 170 lbs and a standard deviation of 15 lbs.

(a) What is the probability that the total weight for this sample of 16 adult males will exceed 2900 lbs? Hint: This is the same as calculating the probability that the average weight for a random sample of 16 exceeds 2900/16.

(b) Will the probability calculated above apply if 16 members from the Blue Hens football team were to get onto the same elevator? Why or why not?

(c) 95% of average weights in a random sample of 16 adult males will exceed _______ ?

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Problem 2

The adult male height follows the normal distribution with a mean of 70 inches, and a standard deviation of 4 inches.

(a) What is the probability that an individual male selected at random is more than 74 inches tall?

(b) What is the probability that the average height for a group of 4 randomly selected males exceeds 74 inches?

(c) Why are the answers to parts (a) and (b) different? How large of a random sample would we need to reduce the standard error to 0.25 inches?

Problem 3

Historical data suggests that the proportion of left handed people is between 7 to 10%. We decide to take a random sample of people to confirm this.

(a) How large would our sample have to be, so that the standard error would be no larger than 1% assuming that the true proportion of left handed people in the general population is 7%?

(b) How large would our sample have to be, so that the standard error would be no larger than 1% assuming that the true proportion of left handed people in the general population is 10%?