Question

Assume that adults have IQ scores that are normally distributed with a mean of 102.5 and a standard deviation 15.7. Find the first quartile Upper Q 1​, which is the IQ score separating the bottom​ 25% from the top​ 75%. (Hint: Draw a​ graph.)

The first quartile is

Answer 1

Solution:-

Given that,

mean = = 102.5

standard deviation = = 15.7

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 = -0.6745

Using z-score formula,

x = z * +

x = -0.6745 * 15.7+102.5

x = 91.9104

First quartile =Q1 = 92