A researcher reports that the time (in minutes)it takes children who are "picky eaters" to finish their vegetables is negatively skewed,with children finishing their vegetables in 4.2 ± 1.0 (M ± SD)min.Based on Chebyshev's Theorem,we can conclude that
A) 68% of children finished their vegetables in 3.2-5.2 min.
B) 50% of children finished their vegetables in at least 3.2 min.
C) 99.7% of children finished their vegetables in 2.2-6.2 min.
D) At least 89% of children finished their vegetables in 1.2-7.2 min.

Question

Quizplus · Accepted Answer

Chebyshev's Theorem states that for any distribution, at least $1 - \frac{1}{k^2}$ of the data values will fall within k standard deviations from the mean. For $k = 3$, this gives $1 - \frac{1}{3^2} = 1 - \frac{1}{9} = \frac{8}{9}$, or at least 89% of the data. Here, 3 standard deviations from the mean (4.2) in both directions cover the range 1.2 to 7.2 minutes.

A Researcher Reports That the Time (In Minutes)it Takes Children