. Bill’s car gets an average of 24.5 miles per gallon (mpg) with a standard devi

Question

. Bill’s car gets an average of 24.5 miles per gallon (mpg) with a standard deviation of 0.6 mpg. On a recent trip to Kansas City his car averaged 26.4 mpg. Did Bill’s car get an unusually high number of mpg during the trip?

(a) Yes, because 26.4 mpg is more than 3 standard deviations above average.

(b) Yes, because 26.4 mpg is 1.9 standard deviations above average.

(c) No, because 26.4 mpg is more than 3 standard deviations below average.

(d) No, because 26.4 mpg is not that far above average.

(e) No, because 26.4 mpg is not that far below average.

Explanation / Answer

26.4 mpg - 24.5 mpg = 2.1 mpg = 3*(0.7) mpg > 3*(0.6) mpg .

So, we observe that this value is certainly an unusually high number as it is more than 3 times the standard deviation above the usual average 24.5 mpg .

So, (a) Yes, because 26.4 mpg ..... average .

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