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) = 6.86 hours and sd(x) = 1.15 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 6.55 and 6.92. (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 6.55 and 6.92. (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 6.55 and 6.92. (use 4 decimal places in your answer)