Suppose Blue Cab Company charges $2.85 a ride up to 0.1 miles and $0.30 for each additional tenth of a mile. If the mean distance a passenger wants to go is 5.3 miles with a standard deviation of 1.4 miles, what is the standard deviation of the fare passengers pay? $0.42 $4.20 $9.00
Question
Suppose Blue Cab Company charges 0.30 for each additional tenth of a mile. If the mean distance a passenger wants to go is 5.3 miles with a standard deviation of 1.4 miles, what is the standard deviation of the fare passengers pay? 4.20 $9.00
Solution
The fare for a ride is a linear function of the distance traveled. The fare is calculated as 0.30 for each additional tenth of a mile.
The standard deviation of the fare can be calculated by multiplying the standard deviation of the distance by the rate of $0.30 per tenth of a mile.
First, convert the distance standard deviation from miles to tenths of a mile: 1.4 miles * 10 = 14 tenths of a mile.
Then, multiply this by the rate: 14 * 4.20.
So, the standard deviation of the fare passengers pay is $4.20.
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