Hi, I need help in below question -

A book club is planning to conduct a telephone survey to estimate the proportion of members of the club who would be inclined to enroll in a new service specializing in cassette-tape recordings of books. The book club would like to estimate this proportion to within plus or minus 5 percentage points at the 95% confidence level.

(a) What is the size of the sample that would need to be surveyed?

(b) Suppose that the book club has decided to call 500 randomly selected members to perform the telephone survey. Suppose that there is a 10% chance that any randomly selected member will not answer the telephone. Let X be the number of randomly selected members among the 500 who will answer the telephone call. What is the distribution of X?

(c) What is the expected value of X?

(d) What is the standard deviation of X?

(e) What is the approximate probability that X is larger than 400?