5.3.25 Question Help When a customer places an order with a certain company\'s o

Question

5.3.25 Question Help 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 the customer has exceeded his or her credit limit. Past records indicate that the probability of customers exceeding their credit limit is 0.07. Suppose that, on a giv day, 23 customers place orders. Assume that the number of customers that the AIS detects as having exceeded their credit limit is distributed as a binomial rando 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 is 1.61 (Round to four decimal places as needed.) The standard deviation is 1.224 customers. Round to three decimal places as needed.) b. What is the probability that 0 customers will exceed their limits? (Round to four decimal places as needed.)

Explanation / Answer

a)

For binomial distribution

Mean = np = 23 * 0.07

= 1.61 ( rounded to two decimal places)

Standard deviation = sqrt( np (1-p) )

= sqrt ( 23 * 0.07 * 0.93)

= 1.224 ( rounded to three decimal places)

b)

p(x) = nCx px (1-p)n-x

p( x = 0) = 23C0 0.070 0.9323

= 0.1884

Probability that 0 customers will exceed their limits is 0.1884

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