Asked by kedna Senatus on Sep 23, 2024
Verified
The mean of fifty sales receipts is $65.75 and the standard deviation is $10.55.Using Chebysheff's Theorem,75% of the sales receipts were between $44.65 and $86.85.
Chebysheff's Theorem
A statistical theorem stating that for any data set or distribution, no matter the shape, a minimum proportion of values must lie within a certain number of standard deviations from the mean.
Standard Deviation
A measure of the amount of variation or dispersion in a set of values, indicating how spread out the values are around the mean.
Sales Receipts
Documents that provide proof of a transaction between a buyer and a seller.
- Understand the concept and application of Chebysheff's Theorem.
Verified Answer
For example, if we let k=2, then we know that at least 1 - 1/2^2 = 75% of the data points will fall within 2 standard deviations from the mean.
Given that the mean of the sales receipts is $65.75 and the standard deviation is $10.55, we can calculate the range within 2 standard deviations from the mean:
$65.75 - 2($10.55) = $44.65
$65.75 + 2($10.55) = $86.85
Therefore, using Chebyshev's Theorem, we can conclude that at least 75% of the sales receipts fall within the range of $44.65 and $86.85.
Thus, the statement is true and the answer is A.
Learning Objectives
- Understand the concept and application of Chebysheff's Theorem.
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