M1 Sampling Distribution

The proportion of defective apples in a farm is y. A sample of n apples is randomly selected from the farm. Let P be the proportion of defective apples in the sample.

(a) Express the standard deviation of P in terms of y and n.

(b) Show that y (1-y) ≤ 0.25

(c) Hence suggest a sample size to ensure that the standard deviation of P is less than 0.04.