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Chebyshev's theorem

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BIG Corporation produces just about everything but is currently interested in the lifetimes of its batteries, hoping to obtain its share of a market boosted by the popularity of portable CD and MP3 players. To investigate its new line of Ultra batteries, BIG randomly selects 1000 Ultra batteries and finds that they have a mean lifetime of 919 hours. Suppose that this mean applies to the population of all Ultra batteries. Complete the following statements about the distribution of lifetimes of all Ultra batteries.

According to Chebyshev's theorem, at least ? of the lifetimes lie within 1.5 standard deviations of the mean, 919 hours.

Suppose that the distribution is bell-shaped. If approximately 99.7% of the lifetimes lie between 664 and 1174 hours, then the approximate value of the standard deviation for the distribution, according to the empirical rule, is ?.

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Solution Summary

This solution gives the step by step method for computing probability based on Chebyshev's theorem is discussed in the solution.

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Chebyshev's theorem - standard deviation

A scientific calculator operates on the average 5.3 hour before needing a recharge. According to Chebyshev's theorem, if the operating times have a standard deviation of 0.6 hour.
A. Between what 2 values will at least 75% of the operating times fall?
B. At least what percentage of the operating times will fall in the interval from 3.5 to 7.1 hours?

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