Question

In a set of 400 values, the mean is 121 and the standard deviation is 14. Estimate how many values fall in between each interval
a) 107 – 135
b)93 – 149
c) 79 – 163

Answer 1

a) Both 107 and 135 are 1 standard deviation away from the mean. So by the empirical rule, about 68% of the distribution is in this interval. So 68% of 400 is 0.68*400 = 272 which means that there are roughly 272 values in this interval.
b) Here 95% of the distribution lives because we're now 2 standard deviations away from the mean. So 0.95*400 = 380 values are in this range
c) We're now 3 standard deviations away from the mean. So 99.7% of the values are found here. 0.997 * 400 = 398.8