When a customer places an order with a company who uses a co

When a customer places an order with a company who uses a computerized accounting system, it automatically checks to see if a customer has exceeded their credit limit. Past records indicate the probability of customers exceeding their credit limit is 0.05. Suppose one day, 20 customers place an order. Assume the number of customers the system detects as having exceeded their limit is distributed as a binomial random variable.

a. What are the mean and standard deviation of the numbers of customers exceeding their limit?

b. What is the probability that zero customers will exceed their limits?

c. What is the probability that one customer will exceed their limit?

Solution

p = 0.05

no of das = 20

As x is binomial

Mean = np = 1

Var = npq = 0.95

std dev = 0.9746

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b) P(x=0) = 0.95²⁰

=0.3585

c) P(X=1) = 20C1(0.05)(0.95)⁹

=0.6302