Assume that a normal distribution of data has a mean of 18 and a standard deviation of 3. use the empirical rule to find the percentage of values that lie below 24.

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Mathematics

Lane Stein

26 August, 14:38

Assume that a normal distribution of data has a mean of 18 and a standard deviation of 3. use the empirical rule to find the percentage of values that lie below 24.

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Harper Leblanc · Answer 1

According to the Empirical Rule, 68% of the data in a standard normal distribution lie within 1 std. dev. of the mean; 95% within 2 std. dev., and 99.9% within 3 std. dev. of the mean.

Here the mean is 18 and the std. dev. is 3. 68% of data lie within 18-3 and 18+3, or 15 and 21.

95% lie within two std. dev. of the mean: 18-3 (2) and 18+3 (2), or 12 and 24.

99% lie within three std. dev. of the mean: 18-3 (3) and 18+3 (3), or 9 and 27.

Summing up the areas: 95% + (half of 4%) = approximately 97%.

Approx. 97% of the data lie to the left of 24.