A gym knows that each member, on average, spends 70 minutes at the gym per week, with a standard deviation of 20 minutes. Assume the amount of time each customer spends at the gym is normally distributed.
a. What is the probability that a randomly selected customer spends less than 65 minutes at the gym?
b. Suppose the gym surveys a random sample of 49 members about the amount of time they spend at the gym each week. What are the expected value and standard deviation of the sample mean of the time spent at the gym?
c. If 49 members are randomly selected, what is the probability that the average time spent at the gym exceeds 75 minutes?