1. Thirty percent of all customers who enter a department store will make a purchase. Suppose that 6 customers enter the store and that these customers make independent purchase decisions.

a. Find the probability that exactly 5 customers make a purchase

b. Find that probability that at least 3 customers make a purchase

c. Find the probability that two or fewer customers make a purchase

d. Find the probability that at least one customer makes a purchase.

e. As the manager of the department store, how should store associates persuade customers who enter the store to make a purchase?

2. As the assistant bank manager, you want to provide prompt service for customers at your bank's drive thru window. The bank can currently serve up to 10 customers per 15-minute period without significant delay. The average arrival rate is 7 customers per 15-minute period. Let x denote the number of customers arriving per 15-minute period. Assume this is a Poisson distribution.

a. Find the probability that 10 customers will arrive in a particular 15-minute period.

b. Find the probability that 10 or fewer customers will arrive in a particular 15-minute period.

c. Does your bank have prompt service? Are there ways that your bank can improve their customer service? How?

3. Bank tellers report that when deciding on where to work, career growth, salary and compensation, location and commute, and company culture and values are important factors to them. According to a blog "25 Highest Paying Companies" the mean monthly pay of bank tellers is $4648. Suppose that the monthly pay is normally distributed with a standard deviation of $400. What is the probability that the monthly pay of a bank teller is

a. less than $4000

b. between $4200 and $4800

c. above $5100

d. Ninety nine percent of the monthly pays are higher than what value?