Suppose that populations of men and women have the following summary statistics for their heights (in centimeters):
Mean
Standard deviation
Men
HM = 172
M = 7.2
Women
Uw = 162
ow = 5.4
Both distributions are approximately normal. Suppose we randomly select a man and a woman from each
population, and calculate the difference between their heights. We can assume that their heights are
independent
Find the probability that the woman is taller than the man
You may round your answer to two decimal places
IN
P woman taller

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Step-by-step explanation:

172-162 = 10  

We can find the standard deviation of D by adding the variances of the heights and taking the square root:

σ  

D

2

σ  

D

2

σ  

D

=σ  

M

2

+σ  

W

2

=7.2  

2

+5.4  

2

square root of 81

=9

Representing probability with area

When D= M-W =0, their heights are equal. When the man is taller, D is positive, and when the woman is taller, D is negative. Since we know the distribution of the difference D is normally distributed, the probability that the woman is taller than the man can be found by calculating the shaded area below D=0, in the corresponding normal distribution:

A standard normal curve is plotted on a horizontal axis representing D, that goes from negative 17 to 37. The mean, or mu sub D, = 10. The standard deviations, or sigma sub D = 9. The value 0 is marked. The area under the curve to the left of 0 is shaded, representing the probability that the woman is taller. The area to the right represents the probability that the man is taller.

normalcdf:

lower bound: −9999

upper bound: 0

μ=10

σ=9

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step-by-step explanation:

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