When a truckload of apples arrives at a packing plant a rand

When a truckload of apples arrives at a packing plant, a random sample of 175 is selected and examined for bruises, discoloration, and other defects. The whole truckload will be rejected if more than 8% of the sample is unsatisfactory. Suppose 9% of the apples on the truck do not meet the desired standard. What is the probability that the shipment will be accepted anyway?

Solution

The shipment will be accepted anyway if the sample produces 9% or less defects. Set this up as a Probability like this:

P(X 0.08) = P[z (0.08 - 0.09) / (sqrt[(0.09)(0.91) / 175] = P(z -0.46), now look this up in a Standard Normal table:

P(z -0.46) = 0.3228 or 32.28% probability the shipment will be accepted anyway.