1.A recent survey describes the distribution of daily sleep time among college students as approximately Normal with a population mean = 7.25 hours and a population standard deviation = 1.35 hours.

a)What is the probability that one randomly selected student has daily sleep time larger than 8 hours? Find the probability and support your answer with an appropriate sketch (or StatCrunch output).

b)What is the probability that 3 randomly selected students each sleep more than 8 hours in a day?

c)Suppose we select a random sample of 9 students, what is the probability that their average daily sleep time will be less than 7 hours?

d)If we do not know that the distribution of the daily amount of sleep is normally distributed, can we compute the probability in c) and ensure we are getting an accurate answer? Explain.