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Chapter 6: Q. 41 (page 378)

Refer to Exercise 37. The ferry company鈥檚 expenses are $20per trip. Define the random variable Yto be the amount of profit (money collected minus expenses) made by the ferry company on a randomly selected trip. That is, Y=M鈭�20.

(a) How does the mean of Yrelate to the mean of M? Justify your answer. What is the practical importance of 渭Y?

(b) How does the standard deviation of Yrelate to the standard deviation of M? Justify your answer. What is the practical importance of 蟽Y?

Short Answer

Expert verified

(a)渭Y=渭M-20

The expected loss per trip is $0.65.

(b)蟽Y=蟽M=6.45

The expected costs are expected to vary by about $6.45from the expected loss pf- $0.65per trip.

Step by step solution

01

Part (a) Step 1: Given Information 

Given:

Y=M-20

02

Part (a) Step 2: Explanation 

Result of previous exercise:

渭M=19.35蟽M=6.45

Property mean:

渭aX+b=a渭X+b

Then we can determine the mean for Yif we know the mean of M:

渭Y=渭M-20=渭M-20=19.35-20=-0.65.

03

Part (a) Step 1: Given Information 

Given:

Y=M-20

04

Part (b) Step 2: Explanation 

Property standard deviation:

蟽aX+b=a蟽X

Result of the previous exercise:

渭M=19.35蟽M=6.45

Then we can determine the standard deviation for Y:

蟽Y=蟽M-20=蟽M=6.45

The practical importance is that the fixed costs do not influence the spread of the distribution of money (profit/money collected).

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