Which of the following is least likely to have a nearly Normal distribution?

(a) Heights of all female students taking STAT $001$ at State Tech.

(b) IQ scores of all students taking STAT $001$ at State Tech.

(c) SAT Math scores of all students taking STAT $001$ at State Tech.

(d) Family incomes of all students taking STAT 001 at State Tech.

(e) All of (a)–(d) will be approximately Normal.

In terms of probability distributions, the normal distribution is a continuous distribution of random variables of real value.

When we don't expect the data set to be highly skewed, a data set has nearly a normal distribution.

Data are considered skewed when most of the values are small, while a few unusually large data values are present, or when most of the values are large, but a few unusually small data values are present.

It is unlikely that the distributions of height, IQ, and SAT math scores will be skewed (as most people will have a score near the average) and so these distributions are probably roughly normal.

As a result, we expect the distribution of family incomes to be skewed, since there are probably a few students in the class who have an unusually small income (for example, students who require a scholarship to be able to attend college).

As a result, it is the least likely that family incomes will have a nearly Normal distribution.