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) 356
B) 89
C) 19
D) 23
E) 505

Question

Quizplus · Accepted Answer

To determine the sample size needed for a proportion with a specific confidence level and margin of error, we use the formula: n = (Z^2 * p * (1-p)) / E^2. For 90% confidence, Z is approximately 1.645. Here, p = 0.7 and E = 0.04. Plugging these values into the formula gives approximately 356.

The Manager of an Orchard Expects About 70% of His