A random variable X is normally distributed with mean mu = 100 and standard deviation sigma = 15. What percentage of the population lies within the interval [70, 130] according to the empirical rule?
Answer and explanation
Correct answer: D. 95.4% (approximately 95%)
The interval [70, 130] corresponds to [mu - 2sigma, mu + 2sigma] because 100 - 2(15) = 70 and 100 + 2(15) = 130. By the empirical rule (68-95-99.7 rule) of normal distributions, approximately 95.4% (roughly 95%) of data points lie within two standard deviations of the mean.
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