Question

The distribution of the Iowa Test of Basic Skills (ITBS) vocabulary scores for 7th-grade students in Gary, Indiana is Normal with a mean of 12 and a standard deviation of 3. Using the empirical rule, what percent of ITBS scores are between 3 and 12

Answer 1

49.85% of ITBS scores are between 3 and 12

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 = 12

Standard deviation = 3

The normal distribution is symmetric, which means that 50% of the scores are below the mean and 50% are below.

What percent of ITBS scores are between 3 and 12

12 is the mean

3 = 12 - 3*3

3 is three standard deviations below the mean.

By the Empirical Rule, of the 50% of the measures which are below the mean(below 12), 99.7% are within 3 standard deviations of the mean, that is, above 3.

So

p = 0.5*0.997 = 0.4985

49.85% of ITBS scores are between 3 and 12