Assume that adults have IQ scores that are normally distributed with a mean of 101.9 and a standard deviation 21.5

Question

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

101.9 and a standard deviation 21.5

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 value of Q1 corresponds to the 25th percentile: 25 % of the observations are below this value. to compute the value, we need to go from a probability/area under the normal curve, to a z-value then to the actual value based on the given distribution.

First, we need to determine the z-value that corresponds to .25 in the left tail. Looking at a z_table, the closest area is .2514 which corresponds to a Z value of -0.67.

To go from a z value to an actual value, you need to reaaraange the formula for z-values to solve for X.

X=zσ + μ. σ(std dev) = 21.5. μ (mean) = 101.9

so X value that corresponds to 25th percentile- Q1 = (-.67)*21.5 + 101.9 = 87.495