The owner of a pet store is trying to decide whether to discontinue selling specialty clothes for pets. She suspects that only 10% of the customers buy specialty clothes for their pets and thinks that...

The owner of a pet store is trying to decide whether to discontinue selling specialty clothes for pets. She suspects that only 10% 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.

a) Assuming the pet store owner is correct in thinking that only 10% of her customers purchase specialty clothes for their pets, how many customers should she expect before someone buys a garment for their pet?

b) What is the probability that she does not sell a garment until the 5th customer?

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

d) What is the probability that at least 3 of the first 35 customers buy specialty clothes for their pet?

e) The owner had 275 customers that day. Assuming this was a typical day for his store, what would be the mean and standard deviation of the number of customers who buy specialty clothes for their pet each day?