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Use the 68%-95%-99.7% (empirical rule) rule to answer the following:

Assuming a set of test scores is normally distributed with a mean of 110 and a standard deviation of 12.

a) The percentage of scores between 98 and 122 is
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b) The percentage of scores between 74 and 146 is

The emperical rule states that 68 percent, 95 percent and 99.7 percent of the data will fall between 1,2 and three standard deviationsof the mean respectively. 

Therefore the observations that will lie between 1 standard deviations of the mean will have values between 98 and 122

Those that will be between 2 standard deviations of the mean will fall between two standard deviations of the mean, 86 and 134

and observations which will be bounded between 74 and 146 will be in 3 standard deviations of the mean. 

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