SOLUTION: The average number of calories in a regular-size bagel is 240. If the standard deviation is 38 calories, find the range in which at least 75% of the data will lie. Use Chebyshev's
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-> SOLUTION: The average number of calories in a regular-size bagel is 240. If the standard deviation is 38 calories, find the range in which at least 75% of the data will lie. Use Chebyshev's
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Question 717757: The average number of calories in a regular-size bagel is 240. If the standard deviation is 38 calories, find the range in which at least 75% of the data will lie. Use Chebyshev's Theorem. Answer by Positive_EV(69) (Show Source):
You can put this solution on YOUR website! Chebyshev's Theorem states that at least 1 - 1/k^2 of the observations will be within k standard deviations of the mean. We want the range that 75% of data lie in, so set this equal to 75%:
.75 = 1 - 1/k^2
1/k^2 = .25
4 = k^2
k = 2
Thus, it can be shown that at least 75% of the observations will lie between +/- 2 standard deviations from the mean. The range is (240 +/- 2*38) = 164 to 316 Calories.
