The manager of an orchard expects about 70% of his apples to exceed the weight requirement for
"Grade A" designation. At least how many apples must he sample to be 90% confident of
Estimating the true proportion within ±4%?
A) 89
B) 505
C) 19
D) 23
E) 356

Question

Quizplus · Accepted Answer

To determine the sample size needed for a proportion, the formula n = (Z^2 * p * (1-p)) / E^2 is used, where Z is the Z-score for the confidence level (1.645 for 90%), p is the estimated proportion (0.7), and E is the margin of error (0.04). Plugging in these values gives n ≈ 356.

The Manager of an Orchard Expects About 70% of His