The amount of a waiter's tips follows some right-skewed distribution with mean $7.26 and standard deviation $4.58.

(a) We take a random sample of three of the waiter's customers. Can you calculate the probability that the mean tip for these customers is less than $12.02?
b) If we take a random sample of 35 of the waiter's customers, what is the probability that the mean tip for these customers is greater than $7.69?
(c) If we take a random sample of 45 of the waiter's customers, what is the probability that the mean tip for these customers is between $6.49 and $7.89?

Question

The amount of a waiter's tips follows some right-skewed distribution with mean $7.26 and standard deviation $4.58.

(a)  We take a random sample of three of the waiter's customers.  Can you calculate the probability that the mean tip for these customers is less than $12.02?
b) If we take a random sample of 35 of the waiter's customers, what is the probability that the mean tip for these customers is greater than $7.69?
(c)  If we take a random sample of 45 of the waiter's customers, what is the probability that the mean tip for these customers is between $6.49 and $7.89?

anonymous · Answer

Are the probabilities you calculated in (b) and (c) exact or approximate? Explain.