statistics questions

Kerk

2007-11-16 8:33 am

when a customer places an order with Rudy's On-Line Office Supplies, 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.

更新1:

Suppose that, on a given day, 20 customers place orders. Assume that the number of customers that the AIS detects as having exceed their credit limit is distributed as a binomial random variable. Give your answers correct to the 4 decimal place.

更新2:

A) what are the mean and standard deviation of the number of customers exceeding their credit limits? B) what is the probability that zero customers will exceed their limit?

更新3:

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?

回答 (1)

myisland8132

2007-11-16 9:18 am

✔ 最佳答案

answer
number of customers that the AIS detects as having exceed their credit limit is distributed as a binomial random variable
x~bin(20,0.05)
p(x)
=(nCx)(p)^x(q)^(n-x)
=(20Cx)(0.05)^x(0.95)^(20-x)
(a)
Mean=np=20*0.05=1
Variance=np(1-p)=20*0.05*0.95=0.95
Standard deviation=√0.95= 0.9747
(b)
The probability that zero customers will exceed their limit
=p(0)
=0.95^20
=0.3585
(c)
The probability that one customer will exceed his or her limit
=p(1)
=20(0.05)(0.95)^19
=0.3774
(d)
The probability that two or more customers will exceed their limits
=1-p(0)-p(1)
=1-0.3585-0.3774
=0.2641

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