Elementary Statistics Question

Question

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

102.9 and a standard deviation 22.

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

Need the z-score Zk, such that

Prob ( z < Zk) = 0.25

which is found via REVERSE table look-up

Zk = -0.67448975

THat is Prob( z < -0.67448975) = 0.25 per the table

Zk = (X - mean)/stndDev

Zk * stndDev + mean = X

-0.67448975 * 22 + 102.9 = X

X=88.0612255

That is Prob(X <= 88.0612255) =

Prob(z <= -0.67448975) = 0.25