According to a survey of the top 10 employers in a major city, a worker spends an average of 413 minutes a day on the job. Suppose the standard deviation is 26.8 minutes and the time spent is approximately a normal distribution.
-According to Chebyshev's Theorem,at least what percentage of measurements in a data set will be within two standard deviations of the mean?
A)68%
B)50%
C)25%
D)75%
E)34%

Question

Quizplus · Accepted Answer

Chebyshev's Theorem states that for any dataset (regardless of distribution shape), at least $1 - \frac{1}{k^2}$ of the values will fall within $k$ standard deviations of the mean. For $k = 2$, this gives $1 - \frac{1}{2^2} = 1 - \frac{1}{4} = \frac{3}{4}$ or 75%.

According to a Survey of the Top 10 Employers in a Major