I with this STATISTICS problem that deals with Chebyshev's theorem.

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Chebyshev's theorem can be applied to determine the percentage of adult men at Suny Rockland whose heights fall between 58.6 inches and 68.6 inches, given a mean height of 63.6 inches and a standard deviation of 2.5 inches. The heights 58.6 and 68.6 are each 2 standard deviations away from the mean. By calculating k as 2, Chebyshev's theorem indicates that at least 75% of the data falls within this range. The formula for determining the interval values involves using the mean and standard deviation to find the lower and upper bounds. This approach effectively utilizes the theorem to assess height distribution.
rdapaul
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the heights of adult men at Suny Rockland have mean heights of 63.6 and a standard deviation of 2.5. What does Chebyshev's theorem tell us about the percentage of men whose heights are between 58.6 in. and 68.6 in.?
 
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Since 58.6 and 68.6 are equally distant from the mean, find the number of standard deviations 68.6 is above the mean and then apply Chebyshev's theorem.
 
rdapaul said:
the heights of adult men at Suny Rockland have mean heights of 63.6 and a standard deviation of 2.5. What does Chebyshev's theorem tell us about the percentage of men whose heights are between 58.6 in. and 68.6 in.?

In such type of questions, the best way to handle them is to ask yourself what formula you require to obtain the interval values. This formula is: lower value=mean-k(s.d.) or upper value=mean+k(s.d.). Once you solve for k in either the two equations, you may use the value obtained to get the percentage using Chebyshev's Theorem.
 

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