Question

The probability model below describes the number of repair calls that an appliance repair shop may receive during an hour.

Repair Calls 0 1 2 3

Probability 0.2 0.3 0.4 0.1

On​ average, the shop receives 1.4 calls an​ hour, with a standard deviation of 0.92 calls. Suppose that the appliance shop plans a 7​-hour day.

a) Find the mean and standard deviation of the number of repair calls they should expect in a day.

The mean number of repair calls they should expect in a day is______ The standard deviation of the repair calls they should expect in a day is 0.90. ​

(Round to two decimal places as​ needed.) ​

(b) What assumption did you make about the repair​ calls?
A. The shop is open on weekends.

B. The shop receives the same number of calls each day.

C. Each call lasts less than 1 hour.

D. The hours are independent. ​

(c) Use the mean and standard deviation to describe what a typical 7​-hour day will be like. Assume that a variation of 1 standard deviation is typical.

A typical 7​-hour day will have about __ to ___ repair calls.

​(Round to the nearest integer as needed. Use ascending​ order.) ​

(d) At the end of a​ day, a worker comments​ "Boy, I'm tired. Today was sure unusually​ busy!" How many repair calls would justify such an​ observation? Assume that a variation of 2 standard deviations is unusual. The smallest observation that would be considered unusual is nothing repair calls.

​(Round up to the nearest​ integer.)

Answer 1