Homework SourseUS adult male heights are on average 70 inches 510 with a st
U.S. adult male heights are on average 70 inches (5\'10) with a standard deviation of 4 inches. Adult women are on average a bit shorter and less variable in height with a mean height of 65 inches (5\'5) and standard deviation of 3.5 inches.
Calculate the percentile for the following:
Lebron James who is 80 inches tall.
Tom Cruise who is 67 inches tall
Nicki Minaj who is 62 inches tall
Aisha Tyler who is 72 inches tall
Solution
a) Lebron James:
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 80
u = mean = 70
s = standard deviation = 4
Thus,
z = (x - u) / s = 2.5
Thus, using a table/technology, the left tailed area of this is
P(z < 2.5 ) = 0.993790335 = 99.38th percentile [ANSWER]
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b) Tom Cruise:
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 67
u = mean = 70
s = standard deviation = 4
Thus,
z = (x - u) / s = -0.75
Thus, using a table/technology, the left tailed area of this is
P(z < -0.75 ) = 0.226627352 or 22.66th percentile [answer]
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c) Nicki Minaj:
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 62
u = mean = 65
s = standard deviation = 3.5
Thus,
z = (x - u) / s = -0.857142857
Thus, using a table/technology, the left tailed area of this is
P(z < -0.857142857 ) = 0.195682969 or 19.57th percentile [answer]
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d) Aisha Tyler:
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 72
u = mean = 65
s = standard deviation = 3.5
Thus,
z = (x - u) / s = 2
Thus, using a table/technology, the left tailed area of this is
P(z < 2 ) = 0.977249868 or 97.72th percentile [answer]
