Question

Suppose that weights of college mathematics textbooks in the United States are

       normally distributed with mean µ = 1.25 lbs and variance σ² = 0.25 lb². Find the

       weight that corresponds to Q₁ and interpret this measure of position in the context of

       the problem.

Answer 1

Solution:-

Given that,

mean = = 1.25

standard deviation = =0.25 =0.5

Using standard normal table,

The z dist'n First quartile is,

P(Z < z) = 25%

= P(Z < z) = 0.25  

= P(Z < -0.6745 ) = 0.25

z = -0.67

Using z-score formula,

x = z * +

x = -0.67 * 0.5+1.25

x = 0.915

First quartile =Q1 = 0.915