How do you solve this? Please and thank you

Question

Assume that adults have IQ scores that are normally distributed with a mean of 95 and a standard deviation of 23. Find the first quartile Q1, which is the IQ score separating the bottom 25% from the top 75%.

Answer 1

First find the z-score associated with the bottom 25% = -0.674, because P(z<0.25) = -0.674.

z = (Q1 - mean)/ standard deviation

-0.674 = (Q1 - 95)/23

Q1 = 23 * -0.674 + 95 = 79.498.