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) The interval is within +-1 standard deviation from the mean. 121 + 14 = 135 and 121 - 14 = 107.
b) The interval is within +-2 standard deviations from the mean.
121 + (2 * 14) = 149 and 121 - (2 * 14) = 93.
c) The interval is within +-3 standard deviations from the mean.
121 + (3 * 14) = 163 and 121 - (3 * 14) = 79.
The empirical rule states that about 68.26% of the values will lie within a distance of +-1 standard deviation from the mean, about 95.45% of the values will lie within a distance of +-2 standard deviations from the mean and about 99.73% of the values will lie within a distance of +-3 standard deviations from the mean.

You should be able to finish this problem yourself now.