The mean of forty sales receipts is $69.75 and the standard deviation is $10.25. Using Tchebysheff's Theorem, at least 75% of the sales receipts were between $49.25 and $90.25.

Question

Quizplus · Accepted Answer

Tchebysheff's Theorem states that regardless of the shape of the distribution, at least 1 - (1/k^2) of the data values will fall within k standard deviations from the mean. 
If we let k=2, this means at least 1 - (1/2^2) = 75% of the data values will fall within 2 standard deviations from the mean. 
Using the mean of $69.75 and the standard deviation of $10.25, we can calculate 2 standard deviations above and below the mean as:
$69.75 - 2($10.25) = $49.25
$69.75 + 2($10.25) = $90.25
Therefore, we can conclude that at least 75% of the sales receipts were between $49.25 and $90.25.

The Mean of Forty Sales Receipts Is $69