The document discusses using Chebyshev's inequality to determine what percentage of values in a distribution fall within a certain number of standard deviations from the mean. Specifically, it explains that for a distribution with a mean of 299 and standard deviation of 15, at least 98.77% of values will fall within 9 standard deviations of the mean, between 254 and 344. It also provides a second example of calculating the interval between 245 and 329.

1. Use Chebyshev
Solution
I. ANSWER: Not less than 98.77% [(1 - 1/9²)*100] of the values are within k = 9
standard deviations of the mean = 299. Why???? Chebyshev's inequality (also known as
Tchebysheff's inequality or Chebyshev's theorem) SOURCE:
http://en.wikipedia.org/wiki/Chebyshev%2… STANDARD DEVIATION: s = 15 MEAN: µ =
299 INTEGER VALUE: k = 9 INTERVAL: [µ - v(k) * s, µ + v(k) * s] = [299 - v(9) * 15, 299 +
v(9) * 15] = [254, 344 ] Chebyshev's inequality states that not more than 1/k² of the
distribution's values can be more than k standard deviations away from the mean. And for this
problem, k = 9 which means that not less than 98.77% [(1 - 1/9²)*100] of the values are within k
= 9 standard deviations of the mean = 299. II. ANSWER: [245, 329] =287-3*14 =287+3*14