Suppose that height is a normally distributed variable with mean of 66 inches and a standard deviation of 3 inches. If you select a person at random from the population, what is the probability that the person is between 60 and 72 inches tall?

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Quizplus · Accepted Answer

The problem describes a normal distribution with a mean (μ) of 66 inches and a standard deviation (σ) of 3 inches. The range from 60 to 72 inches is ±2 standard deviations from the mean (66 - 2(3) = 60 and 66 + 2(3) = 72). According to the empirical rule (68-95-99.7 rule) for normal distributions, approximately 95% of the data falls within 2 standard deviations of the mean. Therefore, the probability that a person selected at random is between 60 and 72 inches tall is about 95%.

Suppose That Height Is a Normally Distributed Variable with Mean