The mean score of a placement exam for entrance into a math

The mean score of a placement exam for entrance into a math class is 80, with a standard deviation of 5. Use the Empirical Rule to fill in the following blanks: (Assume the data set has a bell-shaped distribution.)

68% of the data lies between ___ and ____.

95% of the data lies between ____ and ____.

99.7% of the data lies between ____ and ____.

Solution

m = 80

sd = 5

68 % data lies between one sigma limit,

means, (80-5 , 80+5) = (75,85)

95 % data lies between two sigma limit,

means, (80-5*2 , 80+5*2) = (70,90)

99.7 % data lies between three sigma limit,

means, (80-5*3 , 80+5*3) = (65,95)