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 2.5 standard deviations of the mean?
A)16%
B)40%
C)68%
D)60%
E)84%

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 data will fall within $k$ standard deviations of the mean, where $k > 1$. For $k = 2.5$, the formula gives $1 - \frac{1}{2.5^2} = 1 - \frac{1}{6.25} = 1 - 0.16 = 0.84$, or 84%.

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