chebyshev's theorem

Statistics
Tutor: None Selected Time limit: 1 Day

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

Did you know? You can earn $20 for every friend you invite to Studypool!
Click here to
Refer a Friend
...
Feb 15th, 2015
...
Feb 15th, 2015
Dec 6th, 2016
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer