Question

Assume that adults have IQ scores that are normally distributed with a mean of 101 and a standard deviation 24. Find the first quartile Upper Q 1​, which is the IQ score separating the bottom​ 25% from the top​ 75%.

Answer 1

Solution:-

Given that,

mean = = 101

standard deviation = = 24

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 = -0.67 * 24 + 101

x = 84.92

First quartile =Q1 = 84.92