A mean of 100 and q standard deviation of 15 what is the percentage of scores between 70 and 115

Question

Using 68-95-99.7 rule

Answer 1

Rule of 68-95-99.7 means:

68% of the data in a standard normal distribution falls within one standard deviation of the mean
95% of the data in a standard normal distribution falls within two standard deviations of the mean
99.7% of the data in a standard normal distribution falls within three standard deviations of the mean

For this set of data, which has a mean of 100 and a standard deviation of 15, that means:

68% of students will score between 100 - 15 = 85 and 100 + 15= 115 points
95% of students will score between 100 - 2(15) = 70 and 100 + 2(15) = 130 points
99.7% of students will score between 100 - 3(15) = 65 and 110 + 3(15) = 145 points

Now, 68% of students will score between 85 and 115 points (from the "68" part of the rule).

"95" part of the rule says that 95% of students will score between 70 and 130 points. Now 95%-68% = 27% will score between 70-85 and 115-130. So to find out the % that falls between 70 to 85 we need to divide 27% by 2 which is 13.5%.

Therefore, the percentage of scores between 70 and 115 is 13.5 % (for 70-85)+ 68% (for 85-115). This equals to 81.5%! :)