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Chapter 6: Q. 52 (page 358)

Sul茅鈥檚 job is just a few bus stops away from his house. While it can be faster to take the bus to work than to walk, the travel time is more variable due to traffic. The commute time B if Sul茅 takes the bus to work on a randomly selected day has mean 12 minutes and standard deviation 4 minutes. The commute time W if Sul茅 walks to work on a randomly selected day has mean 16 minutes and standard deviation 1 minute. Calculate and interpret the mean of the difference D=B鈭�W in the time it would take Sul茅 to get to work on a randomly selected day?

Short Answer

Expert verified

The resultant difference of mean is渭=鈭�4

Step by step solution

01

Given information

渭B=12蟽B=4渭W=16蟽W=1

B=Bus commuting time

W=when conversing on the way to work

02

Calculations

渭=渭B鈭�渭W=12鈭�16=鈭�4

Because there are two means for two different random variables 渭B=12 and 渭W=16, the mean of the two random variables will be the difference of their means, resulting in a commute time by bus that is on average 4 minutes less than a commute by walking.

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