If the distribution in the above problem is not bell shaped

If the distribution in the above problem is not bell shaped , atleast what percentage of the population will be: a) between 27 and 35 pounds, b) between 23 and 39 pounds, c) between 19 and 43 pounds?

Solution

By chebyshev\'s theorem, there is at least 1 - 1/k^2 of the population within k standard deviations from the mean.

a)

Here,

k = (x - u)/sigma = (35 - 31)/4 = 1

Thus, at least 1-1/1^2 = 0% of the data is between 27 and 35. [ANSWER, 0%]

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b)

Here,

k = (x - u)/sigma = (39 - 31)/4 = 2

Thus, at least 1 - 1/2^2 = 75% of the data is between 27 and 35. [ANSWER, 75%]

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c)

Here,

k = (x - u)/sigma = (43 - 31)/4 = 3

Thus, at least 1 - 1/3^2 = 88.888889% of the data is between 27 and 35. [ANSWER, 88.888889%]