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8. Suppose that the IQ score for a person selected from a certain group of people
is approximately N(; 100). Let X1;X2; : : : ;Xn be a random sample of such IQ
(a) How large should n be so that a 90% con dence interval for  with maximum
error " = 1 is [ x 􀀀 1:645(10)=
n ; x + 1:645(10)=
n ]?
(b) Verify your answer empirically. In particular, simulate 50 random samples
of size n from the normal distribution N(110; 100). Do approximately 90%
of these samples yield a con dence interval that contains  = 110?

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