Question

An investment fund company has a service that allows clients to make money transfers of a accounts to others over the phone. An estimated 3.2 percent of calling customers find the line is busy or kept on hold for so long that they hang up. Management believes that any failure of this type is a loss of clientele valued at $10. Suppose you try to make 2,000 calls in a certain period. to) Find the mean and standard deviation of the number of callers who are busy or hang up. after they are kept waiting. b) Find the mean and standard deviation of the total customer loss that Experience the investment fund company in these 2,000 calls.

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Answer to a math question An investment fund company has a service that allows clients to make money transfers of a accounts to others over the phone. An estimated 3.2 percent of calling customers find the line is busy or kept on hold for so long that they hang up. Management believes that any failure of this type is a loss of clientele valued at $10. Suppose you try to make 2,000 calls in a certain period. to) Find the mean and standard deviation of the number of callers who are busy or hang up. after they are kept waiting. b) Find the mean and standard deviation of the total customer loss that Experience the investment fund company in these 2,000 calls.

$Expert avatar$

Rasheed

4.7

110 Answers

Let's denote:
-

as the number of callers who find the line busy or hang up
-

as the total customer loss in dollars

Given:
- Probability of a caller finding the line busy or hanging up:

p = 0.032

- Number of calls attempted:

n = 2000

- Value of one lost client:

v =

a) Finding the mean and standard deviation of the number of callers who are busy or hang up:
Mean:

E(X) = np = 2000 \times 0.032 = 64

Standard Deviation:

\sigma_X=\sqrt{np(1-p)}=\sqrt{2000 \times0.032 \times0.968}\approx7.87

b) Finding the mean and standard deviation of the total customer loss:
Mean:

E(Y) = X \times v = 64 \times 640

Standard Deviation:

\sigma_Y=\sigma_X\times v=7.90\times79

$\textbf{Answer:}$

a) Mean number of callers who are busy or hang up:

E(X) = 64

, with a standard deviation of

\sigma_X \approx 7.90

.
b) Mean total customer loss:

E(Y)=640

, with a standard deviation of

\sigma_Y=79

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