Assume that women's heights are normally distributed with a mean of 63.6 inches and standard deviation of 3 inches. If 36 woman are randomly selected, find the probability that they have a mean height between 63.6 and 64.6 inches.
Solution :
Given that,
mean =
= 63.6
standard deviation =
= 3
=
/
n = 3/
36 = 0.5
= P[(63.6 - 63.6) /0.5 < (
-
)
/
< (64.6 - 63.6) / 0.5)]
= P(0 < Z < 2)
= P(Z < 2) - P(Z < 0)
= 0.9772 - 0.5
0.4772
Probability = 0.4772
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