In a company made up of 20,000 employees, 4,000 (20%) are enrolled in an optional savings program. The company is considering changing the program and decides to first take a poll of 400 randomly selected employees. In this problem we will look at the sample percentage of employees who are enrolled in the program.

(a) Consider the box model for this problem. The percentage of 1's in the box is: known OR estimated (circle one).

(b) Consider the percentage of employees in the sample who are enrolled in the program.

What is its expected value? __________% What is its standard error? __________%

(c) Use the normal approximation to calculate the chance that the percentage of employees in the sample who are enrolled in the program is between 19% and 21%.

Answer: _____________%

(d) How do you justify using the normal approximation in (c)? (Your answer should include the name of a theorem and one or more numerical comparisons.)