Question

A set of test scores is normally distributed with a mean of 90 and a standard deviation of 20. Use the 68-95-99.7 rule to find the percentage of scores in each of the following categories. What percentage of scores fall within one standard deviation of the mean?

Answer 1

Using the Empirical Rule for a normal distribution, it is found that 68% of test scores fall within one standard deviation of the mean, which here translates to between 70 and 110.

Step-by-step explanation:

The question involves applying the Empirical Rule, also known as the 68-95-99.7 rule, to a normally distributed set of test scores with a given mean and standard deviation. According to this rule, for a bell-shaped, symmetric distribution:

• Approximately 68% of the data falls within one standard deviation of the mean.
• Approximately 95% falls within two standard deviations.
• More than 99% falls within three standard deviations.

For the stated test scores with a mean of 90 and a standard deviation of 20, we can determine that 68% of scores fall within one standard deviation of the mean. This means that 68% of the scores are between 70 (mean - 1 standard deviation) and 110 (mean + 1 standard deviation).