Question

In a survey of men aged 20 - 29 in a certain country, the mean height is 73.4 inches with a standard deviation of 2.7 inches. Find the minimum height in the top 15% of heights.

Answer 1

Given that,

mean = = 73.4

standard deviation = = 2.7

Using standard normal table,

P(Z > z) = 15%

= 1 - P(Z < z) = 0.15  

= P(Z < z ) = 1 - 0.15

= P(Z < z ) = 0.85

z = 1.04

Using z-score formula  

x = z +

x = 1.04*2.7+73.4

x = 76.208

minimum height in the top 15% of heights is 76.208 inches

Answer 2

SOLUTION :

Let the minimum height in top 15% be “a”  inches.

So,

P(x > a) = 0.15

=> P(x < a) = 1 - 0.15 = 0.85

=> P(z < (a - 73.4)/2.7) = 0.85

So,

Cut-off z = (a - 73.4)/2.7) 

From cumulative ND table , z = 1.0365 

=> (a - 73.4)/2.7) = 1.0365

=> a = 1.0365*2.7 + 73.4

=> a = minimum height = 76.1985 = 76.2 inches approx. (ANSWER)