Suppose that the middle 68 of families of a certain demograp

Suppose that the middle 68% of families of a certain demographic monthly food expenditures fall between 293.45 and 315.73. Give an approximate estimate of the standard deviation of the expenditures. Assume the expenditures have a normal distribution.

Solution

By empirical rule, there are 68% of data within 1 standard deviation from the mean.

Thus, if u = mean, s = standard deviation.

u- s = 293.45
u + s = 315.73

Thus,

s = (315.73 - 293.45)/2 = 11.14 [answer]