Answer to Question #150587 in Statistics and Probability for Vladimyr Lubin

Question

(6.2.18) Assume that adults have IQ scores that are normally distributed with a mean of 101.2 and a standard deviation 20.7. Find the first quartile Q1​, which is the IQ score separating the bottom​ 25% from the top​ 75%. (Hint: Draw a​ graph.)
The first quartile is

Answer 1

P(x<X)=0.25

using table, z score=-0.67

(x-mean)/sd=-0.67

(x-101.2)/20.7=-0.67

x-101.2=20.7*(-0.67)

x-101.2=-13.869

x=87.3

The first quartile is 87.3