Question

Assume that adults have IQ scores that are normally distributed with a mean of

97.8

and a standard deviation

21.2

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

​(Type an integer or decimal rounded to one decimal place as​ needed.)

Answer 1

Given that, mean (μ) = 97.8 and

standard deviation = 21.2

X ~ N(97.8, 21.2)

We want to find, the value of x such that, P(X < x) = 0.25

First we find, the z-score such that, P(Z < z) = 0.25

Using standard normal z-table we get, z-score corresponding probability of 0.25 is z = -0.67

Therefore, the first quartile is 83.6