The heights of American men aged 18 to 24 are normally distributed with a mean o
ID: 3237376 • Letter: T
Question
The heights of American men aged 18 to 24 are normally distributed with a mean of 68 and a standard deviation of 2.5 inches. Answer the following questions.
Half of all young men are taller than ?
About 95% of all young men have heights between ?
What is the probability that a man selected at random will have a height above 72 inches? Use your standard score table.
Suppose you took a sample of 49 men, what is the probability that their mean height is greater than 67 inches? Use your standard score table.
Explanation / Answer
Mean = 68
Deviation = 2.5
a.
Half of all young men are taller than ) = Mean of the distribution = 68
So, 1/2 of young men are taller than 68
b.
About 95% of all young men have heights between +/-Z*SE
=68 +/- 1.96*2.5
= 63.1 to 72.9
c. P(X>72)
= P(Z> 72-68 / 2.5)
= P(Z>4/2.5)
= 1-.9452
= .0548
d.
n = 49
P(X>67)
= P(Z> (67 -68) / (2.5/sqrt(49))
= P(Z>-2.8)
= 1-.0026
= .9974
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