Question

Question 1

Using practical examples from the field of statistics, determine the following variables you expect to have a normal or nearly normal distribution. Illustrate by discussing and explaining possible reasons for your answer.

a. Scores on a very easy test

b. Shoe sizes of a random sample of adult women

c. The number of apples in each of 100 full bushel baskets

Answer 1

1.Normal distributions are bell-shaped and symmetric. The mean, median, and mode are equal. Most of the members of a normally distributed population have values close to the mean—in a normal population 96 percent of the members are within 2 σ of the mean.

a. Normal distribution; since the test is very easy, many people can take scores close to maximum.

b. Normal distribution; most of adult women have shoe sizes in small definite range.

c. Normal distribution; each busket has same volume, so there is no big difference of the number of apples in the baskets.