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) 3 10 15 10 6 2 4 10 The expected value of the waiting time for a random call is most nearly: 7.3 minutes 9.2 minutes 11.5 minutes 15.0 minutes

Answer 1

Solution
We are given that: 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

We have to find expected value of of the waiting time for a random call.

Number of Calls x	Waiting time, minutes f(x)	f(x) * x
0	0	0
2	3	6
4	10	40
6	15	90
8	10	80
10	6	60
$\sum x=30$		$\sum f(x) \times x=276$

Thus

$E(f(X))=\frac{\sum f(x) \times x}{\sum x}$

$E(f(X))=\frac{276}{30}$

$E(f(X))=9.2$

Thus correct option is second option = 9.2 minutes.