What is the probability that the lifetime of a fan exceeds the mean value by more than 3 standard deviations?

Question

Mathematics

Martin Eaton

14 August, 04:57

What is the probability that the lifetime of a fan exceeds the mean value by more than 3 standard deviations?

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Daniella Ward · Answer 1

68.2 % of the data is within one σ, either side of the mean

95.4 % of the data is within two σs, either side of the mean

99.7 % of the data is within three σs, either side of the mean

Therefore, 0.3 % of values lie outside the range of value of three σs.

We can say this is representative of the chance that a value (in this case, the lifetime of the fan) will exceed the mean value by more than three σs.