Taller than one hundred eighty-five

Question

Adult heights in a population follow a normal distribution with a mean of 170 cm and a standard deviation of 10 cm. What is the probability that a randomly chosen adult is taller than 185 cm?

Accepted Answer

Convert the height to a z-score, which measures how many standard deviations it lies above the mean: z = \frac{x - \mu}{\sigma}. For x = 185, mean \mu = 170, spread \sigma = 10, z = \frac{185 - 170}{10} = 1.5. So 185 cm is 1.5 standard deviations above average. The standard normal table gives the area to the left of z = 1.5 as about 0.9332, so 93.32% of adults are shorter than 185 cm. The chance of being taller is the leftover tail: P(X 185) = 1 - 0.9332 = 0.0668. Roughly 6.7% of adults exceed 185 cm. Because 1.5 standard deviations is less extreme than 2, this tail is fatter than the 2.3% we…

Taller than one hundred eighty-five

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