Question

Lottery In Florida’s Play 4 lottery game, four digits between 0 and 9 inclusive are randomly selected each day. We normally expect that each of the 10 different digits will occur about 1/10 of the time, and an analysis of last year’s results shows that this did happen. Because the results are what we normally expect, is it correct to say that the distribution of selected digits is a normal distribution?

Short answer

No, the literal meaning of the word “normal” does not hold valid for normal distribution. Thus, distribution of the digits does not follow a normal distribution. Instead, it will be uniform.

Step-by-step solution

Given information

Four digits are selected at random from 10 digits, 0 to 9, in a lottery.

It is normally expected that each digit has a chance of $\frac{1}{10}$ to be selected.

Explain normal distribution

A dataset is said to be normally distributed if the frequency of the variable is low initially, peaks gradually, and then decreases progressively.

In other words, if the data has a bell-shaped histogram (symmetric), then it follows the normal distribution.

Correct interpretation of the word “normal”

The term “normal” here refers to the most common belief about the occurrence of the digits.

This does not imply that the selection of digits is normally distributed as the word “normal” in a normal distribution is different from the literal meaning of the word normal, which is usual/common.

Since each of the digits has the same 0.1 probability of being selected, the histogram of this data would be even over the range of numbers 0 to 9. This means that the selected digits will follow a uniform distribution.

As a normal distribution has a bell-shaped curve, the distribution of the selected digits will follow a uniform distribution and not a normal distribution.

Thus, it is not correct to state that the distribution of digits is a normal distribution.