Question

Normal Distributions. In Exercises 9 and 10, using a loose interpretation of the criteria for determining whether a frequency distribution is approximately a normal distribution, determine whether the given frequency distribution is approximately a normal distribution. Give a brief explanation.

Best Actors Refer to the frequency distribution from Exercise 6

Short answer

As the frequencies begin from a small value, attain a peak, and then continue to decline and appear to be symmetric, it can be said that the given frequency distribution follows the normal distribution.

Step-by-step solution

Given information

Data are given on the ages of the best actors when they won the Oscar.

Normal distribution

A frequency distribution is considered to follow the normal distribution if the frequencies gradually increase from a small value, achieve a maximum value, and then the frequencies gradually decline.

Also, the frequencies on either side of the peak value should appear to be symmetric.

Here, the following frequency distribution is considered:

Age (years) of the best actors when the Oscar was won	Frequency
20-29	1
30-39	28
40-49	36
50-59	15
60-69	6
70-79	1

It can be observed that the frequencies start from a low value, reach the highest value of 36,and then continue to decrease eventually.

Also, the gradual rise of values before the maximum value and the gradual decline of the values after the maximum value appear to be symmetric.

Therefore, the frequency distribution of the ages of the best actors is normally distributed.