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) = 6.8 hours and SD(X) = 1.21 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 6.75 and 6.93.
(use 4 decimal places in your answer)