chebyshev's theorem

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Given number of batteries = 1000

mean lifetime = 827 hours

standard deviation = 83 hours

According to Chebyshev's theorem, at least 36% of the lifetimes lie between ? hours and ? hours 

round to the nearest integer. 

Feb 15th, 2015

Chebyshev's inequality states that P( |X - u| >= ks) = 1/(k^2) where u is the mean, s is the standard deviation and k is a real number. 

If P = 36% then 1/(k^2) = 0.36  => k = 1.67

So |X - 827| >= (1.67)(83)

hence      827 - (1.67)(83) <= X <= 827 + (1.67)(83)

therefore at least 36% of the lifetimes lie between 688.67 and 965.33 hours. 

Feb 15th, 2015

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Feb 15th, 2015
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