Empirical Rule Worksheet
A Grade 10 math worksheet covering the Empirical Rule (68-95-99.7 rule) for normally distributed data, including problems on percentages, standard deviations, and data interpretation.
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Empirical Rule Worksheet
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Read each question carefully and apply the Empirical Rule (68-95-99.7 rule) to solve the problems. Assume all data sets are normally distributed.
1. In a normal distribution, what percentage of data falls within:
a) 1 standard deviation of the mean?
b) 2 standard deviations of the mean?
c) 3 standard deviations of the mean?
2. The scores on a math test are normally distributed with a mean of 75 and a standard deviation of 5.
a) Approximately 68% of students scored between and .
b) Approximately 95% of students scored between and .
c) Approximately 99.7% of students scored between and .
3. A normally distributed data set has a mean of 50 and a standard deviation of 10. What percentage of the data falls between 30 and 70?
68%
95%
99.7%
99%
4. The average height of adult males in a certain city is 70 inches with a standard deviation of 3 inches. Using the Empirical Rule, estimate the range of heights for the middle 95% of adult males.
5. The Empirical Rule can be applied to any data distribution, regardless of its shape.
True
False
6. On the normal distribution curve below, label the mean and the points representing 1, 2, and 3 standard deviations from the mean. Shade the area representing 68% of the data.