A weight within one standard deviation

Question

Adult weights are normally distributed with a mean of 70 kg and a standard deviation of 5 kg. Use the empirical (68-95-99.7) rule.

What is the probability that a randomly chosen adult weighs between 65 and 75 kg?

Accepted Answer

The empirical rule summarizes the bell curve in whole standard-deviation steps: - 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. Check the endpoints against the mean of 70 kg with a spread of 5 kg. The value 65 kg is \frac{65 - 70}{5} = -1 standard deviation, and 75 kg is \frac{75 - 70}{5} = +1 standard deviation. So the band from 65 to 75 kg is exactly "within 1 standard deviation of the mean." By the rule, that band captures about 68% of adults: P(65 \le X \le 75) \approx 0.68. No tail s…

A weight within one standard deviation

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