5. The owner of a pet store is trying to decide whether to discontinue selling clothes for pets. She suspects that only 5% of the customers buy specialty clothes for their pets and thinks that she might be able to replace the clothes with more interesting and profitable items on the shelves. Before making a final decision she decides to keep track of the total number of customers for a day, and whether they purchase specialty clothes for their pet. The owner had 250 customers that day.

(a) What would be the mean and the standard deviation of the number of customers who buy specialty clothes for their pet each day?

(b) What is the probability that exactly 4 of the first 10 customers buy specialty clothes for their pet?

(c) What is the probability that at least 3 of the first 10 customers buy specialty clothes for their pet?