As a statistician, you are asked to give advice on designing a customer appreciation event for the bookstore. The bookstore plans to put one blue ball and nine red balls in a black box. If a customer draws the blue ball from the box they are awarded a bookstore gift card. They expect that 400 customers will participate in the event. After each draw the ball is replaced in the black box.
(a) Identify the mean and the standard deviation of the proportion of the customers who manage to pick the blue ball among the 400 customers.
(b) How many gift cards should they have in order to have enough gift cards prepared with at least 97.5% probability to award every customer who picks the blue ball?