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

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Percentage of scores less than 100

Relative frequency of scores less than 120

Percentage of scores less than 140

Percentage of scores less than 80

Relative frequency of scores less than 60

Percentage of scores greater than 120

mu = 100, sigma = 20

z = (x – mu)/sigma

(a) x = 100

z = (100 – 100)/20 = 0

Percentage of scores less than 100 = 100 * P(x < 100) = 100 * P(z < 0) = 100 * 0.5 = 50%

(b) x = 120

z = (120 – …

This solution provides the simple calculations to find the required quantities.