a)
Given = 75, = 12.5
We convert this to standard normal as
P(X < x) = P( Z < x - / )
So,
P( X < 82) = P( Z < 82 - 75 / 12.5)
= P( Z < 0.56)
= 0.7123
b)
The central limit theorem is
P( < x) = P(Z < x - / / sqrt(n) )
So,
P( < 82) = P( Z < 82 - 75 / 12.5 / sqrt(25) )
= P( Z < 2.8)
= 0.9974
c)
Normal distribution is used in part b) because,
Since the original population has a normal distribution, the distribution of sample mean is a
normal distribution for any sample size.
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