When mrs. myles gave a test, the scores were normally distributed with a mean of 72 and a standard deviation of 8. this means that 95% of her students scored between which two scores?

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23-12-2016
Mathematics

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When mrs. myles gave a test, the scores were normally distributed with a mean of 72 and a standard deviation of 8. this means that 95% of her students scored between which two scores?

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Jim4109 Jim4109 · Answer 1 · 2016-12-23T13:14:44+01:00

the empirical rule states that in a normal distribution,
68% of data is within 1 std deviation of the mean
95% of data is within 2 std deviation of the mean
99.7% of data is within 3 std deviation of the mean

In this case 95% of the cases would be within two std deviations of the mean
mean - 8 and mean + 8
72 - 8 = 64 and 72 + 8 = 80

then 95% of the scores are between 64% and 80% on the test.