Question

Use the empirical rule to solve the following problems below (DO NOT use the online

calculators to solve these problems) Assume all the data follow the normal distribution:

2. The scores on a standardized test are normally distributed with a mean of 75 and a standard deviation of 10. Find the range of scores that includes the middle 68% of the
test-takers.

Answer 1

To find the range of scores that includes the middle 68% of test-takers, calculate one standard deviation above and below the mean.

Step-by-step explanation:

To find the range of scores that includes the middle 68% of test-takers, we can use the empirical rule. According to the empirical rule, approximately 68% of the data lies within one standard deviation of the mean. Given that the mean is 75 and the standard deviation is 10, we can calculate the range as follows:

1. Find the value one standard deviation below the mean: 75 - 10 = 65
2. Find the value one standard deviation above the mean: 75 + 10 = 85
3. Therefore, the range of scores that includes the middle 68% of test-takers is from 65 to 85.