Statistics and probability question

Question

Assume that adults have IQ scores that are normally distributed with a mean of 99.2 and a standard deviation 19. Find the first quartile Q1, which is the IQ score departing the bottom 25% from the top 75%.

Answer 1

Let x = IQ score

z-score corresponding to 25th percentile is -0.67

z-score = (x - mean)/SD

here z-score is -0.67, mean = 99.2 and SD = 19

substituting:

-0.67 = (x - 99.2)/19

solve for x to find Q1