The heights of the adults in one town have a mean of 671 inc

The heights of the adults in one town have a mean of 67.1 inches and a standard deviation of 3.4 inches.
What can you conclude from Chebyshev\'s theorem about the percentage of adults in the town whose
heights are between 60.3 and 73.9 inches?
A) The percentage is at most 75%. B) The percentage is at least 88.9%
C) The percentage is at most 88.9% D) The percentage is at least 75%

Solution

A)

Chebyshev\'s theorem states that at least 1 - 1/k^2 of the population lies within k standard deviations from the mean.

Here, both 73.9 and 60.3 are 2 standard deviations from the mean. [(60.3 - 67.1)/3.4 = -2, (73.9 - 67.1)/3.4 = 2]

Thus, it contains at least 1 - 1/2^2 = 3/4 = 0.75 = 75% of data.

[OPTION D, AT LEAST 75%]