Question

The waiting times on hold for a call to a customer service department are observed to have the following probability distribution:

Number of calls, x Waiting time, minutes, f(x)
0 0
2 3
4 10
6 15
8 10
10 6

The expected value of the waiting time for a random call is most nearly: ________

a. 7.3 minutes
b. 9.2 minutes
c. 11.5 minutes
d. 15.0 minutes

Answer 1

b. 9.2 minutes

Explanation:

To find the expected waiting time for a random call from the sampie given by using the formula:

`\sum (f(X)) = (\sum f (x) * x)/(\sum x)`

number of calls (x) waiting time f(x) in minutes f(x) *(x)

0 0 0

2 3 6

4 10 40

6 15 90

8 10 80

10 6 60

`\sum x = 30`
`\sum f(x) *x = 276`

Therefore:

`\sum (f(X)) = (276)/(30)`

`\sum (f(X)) = 9.2`