Assume that the heights of men are normally distributed with a mean of 70.8 inches and a standard deviation of 4.5 inches. If 45 men are randomly selected, find the probability that they have a mean height greater than 72 inches.
(Round
your answer to three decimal
places.)
Solution :
Given that ,
mean =
= 70.8
standard deviation =
= 4.5
n = 45
= 70.8
=
/
n = 4.5 /
45 = 0.67
P(
>72 ) = 1 - P(
<72)
= 1 - P[(
-
) /
< (72-70.8) /0.67 ]
= 1 - P(z <1.79 )
Using z table
= 1 - 0.9633
= 0.0367
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