Question

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

100.7100.7

and a standard deviation

19.419.4.

Find the first quartile

Upper Q 1Q1​,

which is the IQ score separating the bottom​ 25% from the top​ 75%. (Hint: Draw a​ graph.)

The first quartile is

nothing.

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

Answer 1

Given,

= 100.7 , = 19.4

We convert this to standard normal as

P(X < x) = P(Z < ( x - ) / )

We have to calculate x such that P(X < x) = 0.25

That is

P(Z < ( x - ) / ) = 0.25

From Z table, z-score for the probability of 0.25 is -0.6745

( x - ) / = -0.6745

( x - 100.7) / 19.4 = -0.6745

Solve for x

x = 87.6

Q1 = 87.6