Chapter 2.2, Problem 69E

To determine

To choose the example which is least likely to have a nearly Normal distribution:

Answer to Problem 69E

(e) All of (a)-(d) will be approximately Normal

Explanation of Solution

Given information:

Given the few examples about the students taking STAT 001 at State Tech.

As all the examples are related to heights, IQ score, Math score and Family income respectively, all these are taking continuous range. And the data in every example spread based on the standard deviation. The example assumes to be of large sample. The plot of the data will be in bell shape in each case. will satisfy the near normality, based on the sample size in each example. For large sample size, near normality or asymptotic normality is found. This has been tested for different data by many researchers earlier and it is found to be normal unless sample size is small. Also, for height, frequency of having less height and more height is less and frequency of having medium height is more. This leads to the bell-shaped structure of the frequency curve. A similar explanation can be given to other examples.