Elementary Statistics: A Step-by-Step Approach with Formula Card 9th Edition

Published by McGraw-Hill Education

Chapter 3 - Data Description - 3-2 Measures of Variation - Exercises 3-2 - Page 145: 33

Answer

$94\%$

Work Step by Step

Chebyshev’s theorem The proportion of values from a data set that will fall within k standard deviations of the mean will be at least $1−1/k^2$, where k is a number greater than 1 (k is not necessarily an integer). 33. In a distribution of 160 values with a mean of 72, at least 120 fall within the interval 67–77. $120/160=0.75$ Let $1−1/k^2=0.75$ we have $k=2$ so $2s=5,s=2.5$ Approximately hat percentage of values should fall in the interval 62–82? $k=\frac{82-72}{2.5}=4$ and $1-1/4^2=0.94$

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