Question

Commuting times for employees of a local company have a mean of 63 minutes and a standard deviation of 3 minutes. What does Chebyshev's Theorem say about the percentage of employees with commuting times between 54 minutes and 72minutes?

A. At most 75% of the commuting times should fall between 56.1 minutes and 71.1 minutes.

B. At least 89% of the commuting times should fall between 56.1 minutes and 71.1 minutes.

C. Approximately 89% of the commuting times should fall between 56.1 minutes and 71.1 minutes.

D. At least 75% of the commuting times should fall between 56.1 minutes and 71.1 minutes.

Answer 1

According to Chebyshev's theorem, at least 8/9 of the data lie within three standard deviations of the mean.

Here, the mean is 63 and the standard deviation is 3.

Hence, the 54 and 72 minutes will be (mean - 3*S.D) and (mean + 3*S.D).

And according to the theoram, at least 89% of the data will fall between these 2 values.

Option B is the right answer.