Question

The height of men is a normally distrubuted variable with a mean of 67 inches and a standard deviation of 2.8 inches.

**Round answers to ONE decimal place**

a.) What is the minimum height you could be to be considered in the top 15% of tallest men?

b.) What is the tallest you could be to be considered in the shortest 20% of men?

Answer 1

Solution:-

Given that,

mean = = 67

standard deviation = = 2.8

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

= P(Z <1.04 ) = 0.85  

z = 1.04 ( using z table )

Using z-score formula,

x = z * +

x = 1.04 * 2.8+67

x = 69.9

(B)

Using standard normal table,

P(Z < z) = 20%

= P(Z < z) = 0.20  

= P(Z < -0.84) = 0.20

z = -0.84 Using standard normal z table,

Using z-score formula  

x= z * +

x=-0.84 *2.8+67

x= 64.648

x=64.6