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Chapter 2: Q 31. (page 108)

Taxi! In 2016, taxicabs in Los Angeles charged an initial fee of \(2.85 plus \)2.70 per mile. In equation form, Fare=2.85+2.7(miles). At the end of a

month, a businessman collects all his taxicab receipts and calculates some numerical

summaries. The mean fare he paid was \(15.45with a standard deviation of \)10.20What are the mean and standard deviation of the lengths of his cab rides in miles?

Short Answer

Expert verified

Mean in miles, 渭mi.=4.6667miles

Standard deviation in miles,蟽mi.=3.7778miles

Step by step solution

01

Given information

Fare=2.85+2.7(miles)

Mean, 渭$=$15.45

Standard deviation,SD$=$10.20

02

Calculation

To get the number of miles from the fare, we must first reduce it by 2.85 and then divide the result by 2.7

Since

Fare=2.85+2.7(miles)

That becomes

miles=Fare鈭�2.852.07

Mean :

Because the mean represents the measurement's centre.

When each data value is reduced by 2.85 the measurement's centre is similarly reduced by 2.85

Similarly,

When all data values are divided by 2.7, the measurement's centre is likewise divided by 2.7

Then

The new standard deviation

蟽mi.=蟽$2.7=10.202.7鈮�3.7778miles

Thus,

The standard deviation of the length of the cab ride in miles is 3.7778 miles.

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