Question

The times that a cashier spends processing individual customers' orders are independent random variables with mean 3.5 minutes and standard deviation 3 minutes. Find the number of customers n such that the probability that the orders of all n customers can be processed in less than 2 hours, is approximately 0.1. (Round your answer to the nearest integer.)

Answer 1

26 customers

Explanation:

First: determine the z score from standard normal probability table with an indicative area of 0.1

Z-score from probability table = - 1.28

mean = 3.5 minutes

std = 3 minutes

next determine the Z-score based on the information given in the question

Z = ( std - mean ) / processing time

= ( 3 - 3.5 ) / 2 = -0.25

Finally determine the number of customers

N =
`((-1.28)/(-0.25) )^2` = 1.6384 / 0.0625 = 26.21 ≈ 26 customers