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Statistical Abstracts (117th edition) provides information about the number of registered automobiles, including taxis, by state.

Statistical Abstracts (117th edition) provides information about the number of
registered automobiles, including taxis, by state. The number of registered
automobiles per 1,000 residents follows an approximately normal distribution with
mean m = 514.6 and standard deviation s = 84.6. In the questions below, x =
number of registered automobiles per 1,000 residents.

(a) Find the probability that for a random sample of 4 states the sample mean, x
is between 475 and 525.
(b) Find the probability that for a random sample of 16 states the sample mean,
x is between 475 and 525.
(c) Compare your answers for parts (a) and (b) and give a reason for the
difference.

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