Question

Assume that a set of test scores is normally distributed with a mean of 100 and a standard deviation of 10 . Use the​ 68-95-99.7 rule to find the following quantities. a. The percentage of scores less than 110 is ​%. ​(Round to one decimal place as​ needed.) b. The percentage of scores greater than 110 is nothing ​%. ​(Round to one decimal place as​ needed.)

Answer 1

a) 100 + 10 = 110

110 is one standard deviation above the mean.

According to the empirical rule about 68% of the data fall within one standard deviation from the mean.

So, 34% of the scores fall within the 100 and 110.

50% of the scores fall below the mean.

So the percentage of scores less than 110 = 50% + 34% = 84%

b) 50% of the scores fall above the mean.

34% of the scores fall within 100 and 110.

So the percentage of scores greater than 110 = 50% - 34% = 16%.