)let x1, x2, . . x80 be a random sample of size 80 taken from the population with p. d.f. f(x) = 3x 2 , 0 < x < 1. find the mean and variance of the population and then use the central limit theorem to approximate p(58 ≤ x 80 i=1 xi ≤ 64). show your work.

The krasnapolski is a top-of-the-line hotel in amsterdam, the netherlands. among their many services, they rent bicycles to guests. the bicycle checkout is open 24 hours per day 7 days per week and has 50 bicycles on hand. on average, 10 guests request a bicycle each day, arriving completely randomly at all times of the day during the spring and summer seasons. guests keep bicycles for four days on average, with a standard deviation of two days. how long does a guest on average have to wait for a bike? a. approximately 24 hours b. approximately 0.033 hours c. approximately 4 days d. approximately 47 minutes