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Chapter 2: Q9 (page 48)

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

Expert verified

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

01

Given information

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

02

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.

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