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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

Sagot :

Ajeigbeibraheemidn

Answer:

b. 9.2 minutes

Step-by-step explanation:

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

[tex]\sum (f(X)) = \dfrac{\sum f (x) \times x}{\sum x}[/tex]

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  

[tex]\sum x = 30[/tex]                                                                          [tex]\sum f(x) *x = 276[/tex]

Therefore:

[tex]\sum (f(X)) = \dfrac{276}{30}[/tex]

[tex]\sum (f(X)) = 9.2[/tex]

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