As reported by a recent survey, the mean height of females 20 to 29 years old is

Question

As reported by a recent survey, the mean height of females 20 to 29 years old is mu equals 63.6 inches. If the height is approximately normally distributed with sigma equals 2.9 inches, answer the following questions. (a) What is the percentile rank of a 20- to 29-year-old female who is 59.9 inches tall? 0.90 th percentile (Round to the nearest integer as needed.) (b) What is the percentile rank of a 20- to 29-year-old female who is 70 inches tall? 0.01 th percentile (Round to the nearest integer as needed.) (c) What proportion of 20- to 29-year-old females are between 59.9 and 70 inches tall?

Explanation / Answer

Mean is 63.6 and s is 2.9

z is given as (x-mean)/s

a) P(x<59.9)=P(z<(59.9-63.6)/2.9)=P(z<-1.28) or 1-P(z<1.28), from normal distribution table we get 1-0.8997=0.1003

b) P(x<70)=P(z<(70-63.6)/2.9)=P(z<2.21) , from normal table it is 0.9864

c) P(59.9<x<70)=P(x<70)-P(x<59.9)= 0.9864-0.8997=0.0867

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