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KATRIN_1 [288]
3 years ago
6

Computers from a certain manufacturer have a mean lifetime of 62 months, with a standard deviation of 12 months. The distributio

n of lifetimes is not assumed to be symmetric. Between what two lifetimes does Chebyshev's Theorem guarantee that we will find at least approximately 75% of the computers
Mathematics
1 answer:
Goryan [66]3 years ago
6 0

Answer:

Between 38 and 86 months.

Step-by-step explanation:

Chebyshev Theorem

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by 100(1 - \frac{1}{k^{2}}).

In this question:

Mean of 62, standard deviation of 12.

Between what two lifetimes does Chebyshev's Theorem guarantee that we will find at least approximately 75% of the computers?

Within 2 standard deviations of the mean, so:

62 - 2*12 = 38

62 + 2*12 = 86

Between 38 and 86 months.

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