NOTE: The numerical values in this problem have been modified for testing purpos

Question

NOTE: The numerical values in this problem have been modified for testing purposes. In its Fuel Economy Guide for 2014 model vehicles, the Environmental Protection Agency gives data on 1160 vehicles. There are a number of high outliers, mainly hybrid gas-electric vehicles. If we ignore the vehicles identified as outliers, however, the combined city and highway gas mileage of the other 1134 vehicles is approximately Normal with mean 22 miles per gallon (mpg) and standard deviation 5.2 mpg. 2014 Volkswagen Beetle with a five-cylinder 2.5L engine and automatic transmission has combined gas mileage 25 mpg. What percent (±±0.1) of all vehicles have better gas mileage than the Beetle (use software)?

Explanation / Answer

as we know from normal distribution Z =(X-mean)/std deviation

hence probabilty that vehicle has better gas mileage than the Beetle =P(X>25)

=P(Z>(25-22)/5.2) =P(Z>0.5769) =1-P(Z<0.5769) =1-0.7180 =0.282

therefore 28.2% have better gas mileage than the Beetle

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