Question

The number of Ford Trucks sold in a month at a particular dealership varies from month to month. Suppose the probability distribution below describes monthly truck sales at this dealership.

x	f(x)
8	0.20
10	0.35
14	0.25
20	0.20

a. What is the Expected Value of monthly sales?

b. Calculate the variance and standard deviation of monthly sales.

c. Suppose this dealership makes $1500 profit on each truck sold. What is the expected monthly profit on sales of Ford Trucks?

d. What is the probability that the monthly truck sales at this dealership are at least 10?

Answer 1

(a)

x                  f                        xf                    x² f

8                0.20                    1.6                     12.8

10               0.35                    3.5                      35

14                0.25                  3.5                      49

20                 0.20                  4                         80

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Total                                 12.6                      176.8

Expected Value = E(X) = 12.60

(b) Variance = E(X²) - (E(X))² = 176.8 - 12.60² = 18.04

Standard Deviation =

(c)

Expected monthly profit = 12.60 X $1500 = $$18,900

(d)

To find P(X10)

Z = (10 - 12.60)/4.25 = - 0.6118

Table of Area Under Standard Normal Curve gives area = 0.2291

So,

P(at least 10) = 0.5 + 0.2291 = 0.7291

So,

Answer is:

0.7291