Assume that a set of test scores is normally distributed with a mean of 100 and a standard devaiton of 20. Use the 68-95-99.7 rule to find the following quantities:

Question

a. percentages of scores less than 100
b. relative frequency of scores less than 120
c.percentage of scores less than 140

Answer 1

Here are a few hints:

a. The mean divides a distribution in half: 50% of the distribution is above the mean and 50% of the distribution is below the mean.

b. A score of 120 is one standard deviation above the mean.

c. A score of 140 is two standard deviations above the mean.

I'll let you take it from here.

Answer 2

a. 50%
b. 0.84
c. 97.72%