question archive An automobile manufacturer has a reliable engine for their fuel efficient cars that has a mean fuel economy of 6

An automobile manufacturer has a reliable engine for their fuel efficient cars that has a mean fuel economy of 6

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An automobile manufacturer has a reliable engine for their fuel efficient cars that has a mean fuel economy of 6.00 L/100 km with a standard deviation of 0.25 L/100 km. The population distribution of the fuel economy is normally distributed.

The automobile manufacturer decided to test the engine using a higher octane gasoline to see if it would significantly improve the fuel economy. They tested 16 engines and calculated a mean fuel economy of 5.88 L/100 km.

Explain why we can assume the shape of the sampling distribution of the mean fuel economy of the engine is normal.

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