Question

Oliver’s Organic Food Store is about to purchase a large shipment of apples
from an orchard. Oliver is picky about the size of the apples, and wants the
mean weight among the apples he is about to purchase to be very close to
150 grams.
When the shipment arrives, Oliver will randomly select n = 9 apples and
compute the sample mean weight among them. He has decided that if the
sample mean weight is less than 145 grams or greater than 155 grams, then
he will decline to purchase the shipment.
Oliver does not know that the weight of a randomly selected apple is a
normally distributed random variable with a mean of 151 grams and a
standard deviation of 13 grams.
a) What is the probability that Oliver will decline to purchase the shipment?
b) If Oliver chooses a sample size of n = 22 instead, what is the probability that he will decline to purchase the shipment?

Answer 1