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The fuel consumption, in miles per gallon, of all cars of a particular model has a...

The fuel consumption, in miles per gallon, of all cars of a particular model has a mean of 90 and a standard deviation of 12. The population distribution can be assumed to be normal. A random sample of these cars is taken.

(a) What is the sampling distribution of the sample means?

(b) Find the probability that sample mean fuel consumption will be fewer than 75 miles per gallon if:

i. a sample of 1 observation is taken.

ii. a sample of 4 observations is taken.

iii. a sample of 16 observations is taken.

(c) Explain why the three answers in part (a) differ in the way they do. Draw a graph to illustrate your reasoning.

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