A battery lasting past twelve hours

Question

Battery lives are normally distributed with a mean of 10 hours and a standard deviation of 1 hour. Instead of a z-table, use the empirical (68-95-99.7) rule.

What is the probability that a battery lasts more than 12 hours?

Accepted Answer

The empirical rule is a quick summary of the bell curve using whole numbers of standard deviations from the mean: - about 68% of values fall within 1 standard deviation of the mean, - about 95% within 2 standard deviations, - about 99.7% within 3 standard deviations. Here 12 hours is \frac{12 - 10}{1} = 2 standard deviations above the mean. The rule says 95% of batteries land within 2 standard deviations of 10 hours, that is, between 8 and 12 hours. So 5% fall outside that band, split evenly between the two tails by the curve's symmetry: P(X 12) = \frac{1 - 0.95}{2} = \frac{0.05}{2} = 0.025. …

A battery lasting past twelve hours

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