Customers arrive at a bank according to a Poisson process at the rate of 100 per hour. 20%
of them make only a deposit, 30% make only a withdrawal and the remaining 50% are there
only to complain. Deposit amounts are distributed with mean 8000 and standard deviation
1000. Withdrawal amounts have mean 5000 and standard deviation 2000.
The number of customers and their activities are mutually independent.
Using the normal approximation, calculate the probability that for an 8-hour day the total
withdrawals of the bank will exceed the total deposits.
(A) 0.27
(B) 0.30
(C) 0.33
(D) 0.36
(E) 0.39
这是MLC Sample中的182题，我觉得官方的解答有问题，不知是不是自己的概念错
以下是官方部分解答，有问题的地方我做了注释
Split into three independent processes:
Deposits, with λ* = (0.2)(100)(8) =160 per day
Withdrawals, with λ* = (0.3)(100)(8) = 240 per day
Complaints. Ignore, no cash impact.
For aggregate deposits,
E(D) = (160)(8000) =1,280,000
Var (D) = (160) (1000)^2 + (160) (8000)^2 有问题，方差不是这么算的
=1.04×10^10
For aggregate withdrawals
E(W) = (240)(5000) =1,200,000
Var (W) = (240)( 2000)^2 + (240)( 5000)^2 同样，这里也有问题
= 0.696×10^10
Var (W − D) = 0.696×10^10 +1.04×10^10 =1.736×10^10 这里就更加不对了
求高手指点啊