When a customer places an order with a certain company\'s on-line supply store,

Question

When a customer places an order with a certain company's on-line supply store, a computerized accounting information system (AIS) automatically checks to see 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, 25 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. Complete parts (a) through (d) below. a. What are the mean and standard deviation of the number of customers exceeding their credit limits? The mean number of customers exceeding their credit limits us. The standard deviation is customers. b. What is the probability that 0 customers will exceed their limits? c. What is the probability that 1 customer will exceed his or her limit? d. What is the probability that 2 or more customers will exceed their limits?

Explanation / Answer

here p = 0.05, n = 25 and q = 0.95

(a) mean = np = 0.05*25 = 1.25
std. dev. = sqrt(npq) = sqrt(25*0.05*0.95) = 1.0897

(b)
P(X=0) = q^n = 0.95^25 = 0.2774

(c)
P(X=1) 25C1 * p^1 * q^24 = 25*0.05^*0.95^24 = 0.365

(d)
P(X>=2) = 1 - P(X=0) - P(X=1) = 1 - 0.2774 - 0.365 = 0.3576

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