525 When a customer places ail order with Rudys OnLine Offic

5.25 When a customer places ail order with Rudy\'s On-Line Office Supplies, a computerized accounting in formation system (AIS) automatically checks to sec if the customer has exceeded his or her credit limit. Past records indicate that the probability of customers exceeding their credit limit is 0.05. Suppose that, on a given day, 20 customers place orders. Assume that the number of customers that the AIS detects as having exceeded their credit limit is distributed as a binomial random variable. a. What are tile mean and standard deviation of the number of customers exceeding their credit limits? b. What is the probability that zero customers will exceed their limits? c. What is the probability that one customer will exceed his or her limit? d. What is the probability that two or more customers will exceed their limits?

Solution

A. For the binomial, mean is n*p = 20*0.05 = 1; variance is n*p*(1-p) = 20*0.05*0.95 = 0.95. B. P[x=0] = 0.3585. C. P[x=1] = 0.3774. D. P[x=2] = 0.1887.