Statistics help

Question

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

103.3 and a standard deviation 24.2

Find the first quartile Upper Q 1Q1​, which is the IQ score separating the bottom​ 25% from the top​ 75%.

What is the first quartile?

Answer 1

The first quartile is the number in between the lowest number of a data set and the median. To find it, I would use a Z table such as this one: https://www.ztable.net/ (note: we'll want a negative z score since we're looking at the left side of a normal distribution) I would find the z score that corresponds to 0.25 which is -0.67 on this table.

I would then rearrange the equation of a z score to solve for x: z = (x - μ)/σ to x = zσ + μ where x is the value we're looking for and σ and μ are the standard deviation and the mean given in the problem.

Calculating x = -0.67*24.2 + 103.3 gives us x = 87.1 after rounding to the most significant digit.