Question

A bank official is concerned about the rate at which the bank's tellers provide service for their customers. He feels that all of the tellers work at about the same speed, which is either 30, 40, or 50 customers per hour. Furthermore, 40 customers per hour is twice as likely as each of the other two values, which are assumed to be equally likely. In order to obtain more information, the official observes all five tellers for a two-hour period, noting that 380 customers are served during that period. Use this new information to revise the official's probability distribution of the rate at which the tellers provide service.

Answer 1

Existing customers per teller per hr

We know, 40 customers probability is twice of 30 and 50.

Customers	Weights	Multiply
30	1	30
40	2	80
50	1	50
Sum	4	160
Average		40

New Information

As per observation, 380 customers are services in 2 hrs by 5 tellers

i.e. 38 customers per her per teller

Revised probability distribution.

We observe that it is a normal distribution with equal weights on either sides and middle point being the average expected customers.

i.e We need to revise the expected customers from 40 to 38 (which is recent observation)

Keeping minimum at 30 only, we know mid point is 38. So keeping the difference between upper and mid limit same as differnce between lower and mid point, upper limit would be 46( 38+8)

Revised Distribution

Customers	Weights	Multiply
30	1	30
38	2	76
46	1	46
Sum	4	152
Average		38