Question

Adult men’s heights (in inches) are normally distributed with µ = 69 and σ = 2.8. Adult women’s heights (in inches) are normally distributed with µ = 64 and σ = 2.5. Members of the “Beanstalk Club” must be at least six feet (72 inches) tall.

1. If a man is selected at random, what is the probability that he is eligible for the Beanstalk Club?

2. If a woman is selected at random, what is the probability that she is eligible for the Beanstalk

            Club?

Answer 1

A)

µ =    69              
σ =    2.8              
                  
P ( X ≥   72.00   ) = P( (X-µ)/σ ≥ (72-69) / 2.8)          
= P(Z ≥   1.071   ) = P( Z <   -1.071   ) =   

0.1420

B)

µ =    64              
σ =    2.5              
                  
P ( X ≥   72.00   ) = P( (X-µ)/σ ≥ (72-64) / 2.5)          
= P(Z ≥   3.200   ) = P( Z <   -3.200   ) =   

0.0007

Thanks in advance!

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