According to the Centers for Medicare & Medicaid Services, 21% of nursing homes in the United States received five stars in overall ratings on a scale of 1 to 5. A random sample of seven nursing homes was selected. What is the standard deviation of this distribution?

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Quizplus · Accepted Answer

The standard deviation of a binomial distribution is the square root of np(1-p), where n is the sample size and p is the probability of success. In this case, n = 7 and p = 0.21, so the standard deviation is sqrt(7 * 0.21 * 0.79) = 1.078.