A body temperature above the far cutoff

Question

Resting body temperatures are normally distributed with a mean of $37\,^\circ$ C and a standard deviation of $0.5\,^\circ$ C. Use the empirical (68-95-99.7) rule.

What is the probability that a reading is above $38.5\,^\circ$ C?

Accepted Answer

The empirical rule in standard-deviation steps: - about 68% within 1 standard deviation of the mean, - about 95% within 2 standard deviations, - about 99.7% within 3 standard deviations. The value 38.5\,^\circC is \frac{38.5 - 37}{0.5} = 3 standard deviations above the mean, so we want the extreme high tail beyond 3 standard deviations. The rule says 99.7% of readings fall within 3 standard deviations (between 35.5 and 38.5\,^\circC). That leaves 1 - 0.997 = 0.003 outside, split evenly between the two tails by symmetry. The high tail gets half: P(X 38.5) = \frac{1 - 0.997}{2} = \frac{0.003}{2…

A body temperature above the far cutoff

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