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Which one of the following suggests that the data set is not approximately normal?

1) A data set with 68
2) A data set with 95
3) A data set with 99.7
4) A data set with 100

Answer :

Final answer:

In a data set, a value of 100 indicates that the data set is not approximately normal, as it lies more than two standard deviations away from the mean. option (4) is correct answer.

Explanation:

The data set with 100 suggests that the data set is not approximately normal. To explain this, let's refer to the Empirical Rule, which states that for a normal distribution, approximately 95% of the data falls within two standard deviations of the mean. Therefore, if a data set has a value of 100, it indicates that it is more than two standard deviations away from the mean, deviating from the properties of a normal distribution.

Option 4) 100 suggests that the data set is not approximately normal, as it implies that all data points are within a certain range from the mean, which is inconsistent with the Empirical Rule. The question asks which data set suggests that the distribution is not approximately normal.

The Empirical Rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation from the mean, approximately 95% within two standard deviations, and about 99.7% within three standard deviations. In the options provided, 1) 68, 2) 95, and 3) 99.7 correspond with the Empirical Rule, indicating a normal distribution.

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