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 Actresses Refer to the frequency distribution from Exercise 5

Short answer

As the frequencies do not begin from a small value, attain a peak and then continue to decline, it can be said that the given frequency distribution does not follow the normal distribution.

Step-by-step solution

Given information

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

Normal distribution

A frequency distribution is said to follow the normal distribution if the frequencies gradually increase from a small value, and after reaching a peak, the frequencies gradually decline.

Here, the following frequency distribution is considered:

Age (years) of the best actresses when the Oscar was won	Frequency
20-29	29
30-39	34
40-49	14
50-59	3
60-69	5
70-79	1
80-89	1

It can be observed that the frequencies start from a high value and then continue to decrease till the last class interval.

This suggests that the distribution has a tail towards the right, and hence, it is skewed.

Therefore, the frequency distribution of the ages of the best actresses when they won the Oscar is not normally distributed.