Question

8. A company sells concrete in batches of 5 cubic yards. The probability distribution of X, the number of cubic
yards sold in a single order for concrete from this company, is shown in the table below.
|
X = the number of cubic yards
Probability
10
10.15
15
0.25
20
0.25
25
0.30
30
0.05
The expected value of the probability distribution of X is 19.25 and the standard deviation is 5.76. There
is a fixed cost to deliver the concrete. The profit Y, in dollars, for a particular order can be described by
Y = 75X - 100. What is the standard deviation of Y?
(A) $332.00
(B) $432.00
(C) $532.00
(D) $1,343.75
(E) $1,400.00

Answer 1

Answer:

$432

Step-by-step explanation:

75(5.76)=432

Answer 2

The standard deviation of Y is $432 and this can be determined by using the formula of standard deviation and the given data.

Given :

• A company sells concrete in batches of 5 cubic yards.
• The probability distribution of X, the number of cubic  yards sold in a single order for concrete from this company, is shown in the table below.
• The expected value of the probability distribution of X is 19.25 and the standard deviation is 5.76.
• There  is a fixed cost to deliver the concrete. The profit Y, in dollars, for a particular order can be described by  (Y = 75X - 100).

The formula to obtain the standard deviation is given below:

SD(Y) = SD(75X - 100)

Simplify the above expression by substituting the value of SD(X) and SD(100) in the above expression.

SD(Y) = 75SD(X) - SD(100)

SD(Y) = 75 SD(X) - 0

SD(Y) = 75 $\times$ 5.76

SD(Y) = $432

Therefore, the correct option is B).

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