Incomes of workers in an automobile company in Ontario are known to be right-skewed, with a mean equal to $36,200. Applying Tchebysheff's Theorem, at least 8/9 of all incomes are in the range of $29,600 to $42,800. What is the standard deviation of those incomes from that mean?
A) $2,200
B) $4,755
C) $6,500
D) $6,700

Question

Quizplus · Accepted Answer

Tchebysheff's Theorem states that at least 1 - 1/k^2 of all data values will fall within k standard deviations of the mean. In this case, k = 3, so at least 1 - 1/3^2 = 8/9 of all incomes will fall within 3 standard deviations of the mean. Therefore, the standard deviation must be (42,800 - 29,600) / 6 = $2,200.

Incomes of Workers in an Automobile Company in Ontario Are