The United States Centers for Disease Control and Prevention (CDC) recommends that adults sleep seven to nine hours per night (CDC.gov website).

However, many adults in the United States sleep less than seven hours per night. Suppose that the amount of sleep per night for an adult in the United States follows a normal distribution with a mean of 8.0 hours and standard deviation of 1.7 hours.

a. What is the probability that a randomly selected adult in the United States sleeps less than 7.0 hours per night?

b. What is the probability that a randomly selected adult in the United States sleeps between 7.0 and 9.0 hours per night?

c. How many hours per night would an adult in the United States sleep if they are in the 10th percentile of this distribution?