Question

1. It is estimated that heights of adult men are normally distributed with a mean of 70 inches and a standard deviation 3.3 inches. In one state, the law requires a person to be 68 inches or taller to become a fire fighter.

1. What proportion of adult men will meet this height requirement for becoming a fire fighter in this state? .7291
2. A person who was denied to become a fire fighter learned that his height was at the 20^th percentile. What was his actual height? 70.66 inches

Answer 1

Solution :

Given that,

mean = = 70

standard deviation = = 3.3

P(x >68 ) = 1 - P(x<68 )

= 1 - P[(x -) / < (68-70) /3.3 ]

= 1 - P(z < -0.61)

Using z table

= 1 - 0.2709

= 0.7291

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 *3.3+70

x= 67.228