probabilities

In order to study the corresponding market share of a newly released
smart mobile phone, the marketing manager of the mobile phone
manufacturer has randomly selected a sample of 200 customers from a
large number of people who have shown an interest in owning a smart
mobile phone, and data regarding their preferences for brands of smart
mobile phones were collected.

In an earlier pilot survey, it was estimated that the true proportion of
customers who prefer the company’s smart mobile phone is 0.25. If this estimation is correct, among those 200 customers:


a what are the corresponding mean and the standard deviation of the
sample proportion of customers who prefer the company’s smart
mobile phone?

b what is the probability that the sample proportion of customers who
prefer the company’s smart mobile phone is less than 0.2?