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2. Statistical Abstracts (117th edition) provides information aboutthe number of

ID: 2954643 • Letter: 2

Question

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

(a) Find the probability that for a random sample of 4 statesthe sample mean, x
is between 475 and 525.
(b) Find the probability that for a random sample of 16states 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.


Explanation / Answer

Given xbar=514.6, s=84.6 (a) Find the probability that for a random sample of 4 statesthe sample mean, x is between 475 and 525. P(475
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