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?

Answer 1

Answer: At-least 89% of employees with commuting times between 54 minutes and 72 minutes .

Explanation:

Given: Commuting times for employees of a local company have a mean of 63 minutes and a standard deviation of 3 minutes.

Now, 54 minutes = (63 - 9) minutes

= (63 -3(3)) minutes

= Mean - 3 standard deviation

72 minutes = (63 + 9) minutes

=63 +3(3) minutes

= Mean + 3 standard deviation

According to Chebyshev's theorem, at least
`(8)/(9)` of the data lie within 3 standard deviations of the mean.

i.e. The percentage of employees with commuting times between 54 minutes and 72 minutes =
`(8)/(9)*100\approx89\%`

Hence, at-least 89% of employees with commuting times between 54 minutes and 72 minutes .