Question

Many states assess the skills of their students in various grades. One of the tests provided by a national association assesses the reading skills of 12th-grade students. In a recent year, the national mean score was 286 and the standard deviation was 38. Assuming that these scores are approximately Normally distributed, N(286, 38), use the 68-95-99.7 rule to give a range of scores that includes 95% of these students.

Answer 1

95% of these scores are between 210 and 362.

Explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 286, Standard deviation = 38

Use the 68-95-99.7 rule to give a range of scores that includes 95% of these students.

This is within 2 standard deviations of the mean. So

286 - 2*38 = 286 - 76 = 210

286 + 2*38 = 286 + 76 = 362

95% of these scores are between 210 and 362.