According to the National Center for Health Statistics, 17% of adults between the ages of 45 and 64 had taken statin drugs in the prior 30 days to reduce cholesterol levels. A random sample of 120 adults from this age group was selected. What is the probability that between 24 and 27 from this sample had taken statin drugs during the last 30 days?

Question

Quizplus · Accepted Answer

The probability can be calculated using the binomial distribution formula:P(X = k) = (n! / (k!(n-k)!)) * p^k * (1-p)^(n-k)where:n is the sample size (120)k is the number of successes (between 24 and 27)p is the probability of success (0.17)P(X = 24) = (120! / (24!(120-24)!)) * 0.17^24 * (1-0.17)^(120-24) = 0.1373P(X = 25) = (120! / (25!(120-25)!)) * 0.17^25 * (1-0.17)^(120-25) = 0.1029P(X = 26) = (120! / (26!(120-26)!)) * 0.17^26 * (1-0.17)^(120-26) = 0.0658P(X = 27) = (120! / (27!(120-27)!)) * 0.17^27 * (1-0.17)^(120-27) = 0.0386Therefore, the probability that between 24 and 27 from this sample had taken statin drugs during the last 30 days is:P(24 ≤ X ≤ 27) = P(X = 24) + P(X = 25) + P(X = 26) + P(X = 27) = 0.1373 + 0.1029 + 0.0658 + 0.0386 = 0.3446

According to the National Center for Health Statistics, 17% of Adults