Question

The heights of young women aged 20 to 29 follow approximately the N (64,2.7) distribution. Young men the same age have height distributed as N (69,3,2.8). The height are in inches. Determine each of the following.
a. what percentage of young men have a height of less than 6 feet?
b. what percentage of young women have a height of more then 5 feet.
c. Below what height is 25% of the young men?
d. Above what height is 40% of the young women?

Answer 1

let M: Height of Men

W: height of women

Then W~N(64,2.7)

and M~N(69.3,2.8)

a) 6 feet = 6 *12 iinches = 72 inches.

So, P[M<72]

   Z~N(0,1)

= 0.8315

So, almost 83% young ,man are below 6 feet.

b) P[W>60] = 1- P[W<60]

  

  

So, almost 93% of young women are above 5 feet.

c) we have to find x such that:

  

ie, 25% of men are below the height 67.4 '

d. we have to find y such that :

P[W>y] = 0.40

ie. 40% of the women are above the height 64.7'

I got the values from z table. I hope you have it. If you have doubts, let me know below. Thank you