More than 100 million people around the world are not gettingenough sleep; the average adult needs between 7.5 and 8 hours ofsleep per night. College students are particularly at risk of notgetting enough shut-eye. A recent survey of several thousandcollege students indicated that the total hours of sleep time pernight, denoted by the random variable X, can be approximated by anormal model with E(X) = 6.79 hours and SD(X) = 1.22 hours.Question 1. Find the probability that the hours of sleep per nightfor a random sample of 4 college students has a mean x between 6.62and 6.95. .0039 Incorrect: Your answer is incorrect. (use 4 decimalplaces in your answer) Question 2. Find the probability that thehours of sleep per night for a random sample of 16 college studentshas a mean x between 6.62 and 6.95. (use 4 decimal places in youranswer) Question 3. Find the probability that the hours of sleepper night for a random sample of 25 college students has a mean xbetween 6.62 and 6.95. (use 4 decimal places in your answer)Question 4. The Central Limit Theorem was needed to answerquestions 1, 2, and 3 above.
