Question

According to a study done by De Anza students, the height for Asian adult males is normally distributed with an average of 66 inches and a standard deviation of 2.5 inches. Suppose one Asian adult male is randomly chosen. Let X = height of the individual.

The middle 40% of heights fall between what two values?

Write the probability statement.

P(x₁ < X < x₂) =

State the two values. (Round your answers to one decimal place.)

x1	=
x2	=

Answer 1

X   N( 66, 2.5^2 )

P(x₁ < X < x₂) =
0.40   = --  
Since the normal distribution is said to be a symmetric distribution,
The data below x1 & that above x2 is : 0.10
i.e. P(X > x2 ) = 0.10 & P(X < x1) = 0.10
From Z tables, when z = -1.28 , P( X < z ) = 0.10
& when z = 1.28 , P( X > z ) = 0.10

Thus,
= 1.28 & = -1.28
x2 = 69.2 & x1 = 62.8

Hope this answers your query!