Owners of a weight loss programme want to obtain an indication of the total number of subscriptions to their programme for the current year. People who subscribe to the programme do so through one of the 240 weight loss programme representatives. It is decided that a simple (uniform) random sample (without replacement) of the representatives is to be obtained in order to investigate the total number of subscriptions. A pilot survey conducted from the previous year, indicated that the total number of subscriptions to the programme was thought to be approximately 1,500 and 20.5 was the estimated standard deviation of the number of subscriptions between representatives.

(a) How large a sample of representatives would be needed to enable estimation of the total number of subscriptions to be within 10% of the total obtained from the previous years pilot survey, with 95% certainty?

(b) Define what a pilot survey is and describe three advantages of using such a thing.