Question

The upper leg length of 20- to 29-year-old males is normally distributed with a mean length of 43.7 cm and a standard deviation of 4.2 cm.

(A) Find the probability that a randomly selected a U.S. man who are 20–29 years old has an upper leg length that is less than 40 cm? .

(B) Find the 95th percentile.

(C) What is the probability that a random sample of 9 males who are 20–29 years old results in a mean upper leg length that is less than 40 cm?

Answer 1

Ans:

mean=43.7

standard deviation=4.2

a)

z=(40-43.7)/4.2

z=-0.881

P(z<-0.881)=0.1892

b)P(Z<=z)=0.95

z=normsinv(0.95)=1.645

P95=43.7+1.645*4.2=50.61

c)

z=(40-43.7)/(4.2/sqrt(9))

P(z<-2.64)=0.0041