Question

More than 100 million people around the world are not getting enough sleep; the average adult needs between 7.5 and 8 hours of sleep per night. College students are particularly at risk of not getting enough shut-eye.

A recent survey of several thousand college students indicated that the total hours of sleep time per night, denoted by the random variable X, can be approximated by a normal model with E(X) = 6.94 hours and SD(X) = 1.27 hours.

Question 1. Find the probability that the hours of sleep per night for a random sample of 4 college students has a mean x between 6.71 and 6.95.

(use 4 decimal places in your answer)

Question 2. Find the probability that the hours of sleep per night for a random sample of 16 college students has a mean x between 6.71 and 6.95.

(use 4 decimal places in your answer)

Question 3. Find the probability that the hours of sleep per night for a random sample of 25 college students has a mean x between 6.71 and 6.95.

(use 4 decimal places in your answer)

Question 4. The Central Limit Theorem was needed to answer questions 1, 2, and 3 above.

True or False?

Answer 1

1. Here n=4.

2. Here n=16.

3. Here n=25.

4. Ans : FALSE, because population is itself Normal.