The heights of women aged 20-29 follow approximately the normal distribution wit

Question

The heights of women aged 20-29 follow approximately the normal distribution with a mean 64 inches and a standard deviation of 2.7 inches and men of the same age have heights with mean 69.3 inches, and standard deviation of 2.8 inches.  

a. What percent of females have a height between 58.6 inches and 69.4 inches?

b. What percent of females have a height shorter than 70 inches?

c. What percent of females have a height taller than 70 inches?

d. What percent of young women are taller than the mean height of young men?

Explanation / Answer

a)percent of females have a height between 58.6 inches and 69.4 inches =P(58.6<X<69.4)

=P((58.6-64)/2.7<Z<(69.4-64)/2.7) =P(-2<Z<2)=(0.97725-0.02275) =0.9545 ~ 95.45%

b) percent of females have a height shorter than 70 inches P(X<70)=P(Z<2.2222)=0.9869 ~ 98.69%

c)percent of females have a height taller than 70 inches =P(X>70)=1-P(X<70) =1-0.9869 =0.0131 ~ 1.31%

d) percent of young women are taller than the mean height of young men =P(X>69.3)

=1-P(X<69.3)=1-P(Z<1.9630)=1-0.9752 =0.0248 ~ 2.48%

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