Question

Assume that adults have IQ scores that are normally distributed with a mean of 100.6 and a standard deviation 20.7 Find the first quartile Upper Q1 which is the IQ score separating the bottom​ 25% from the top​ 75%. (Hint: Draw a​ graph.) The first quartile is? Second quartile is?

Answer 1

Solution:-

Given that,

mean = = 100.6

standard deviation = = 20.7

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 = -0.67 * 20.7+100.6

x = 86.731

First quartile =Q1 =  86.73

b )P(Z < z) = 75%

= P(Z < z) = 0.75  

= P(Z < 0.6745 ) = 0.75

z = 0.6745

Using z-score formula,

x = z * +

x = 0.67 * 20.7 +100.6

x = 114.469

Third quartile =Q3 = 114.47