According to the National Health Interview Survey, 4.7% of U.S. adults 50 and older have had a total knee replacement. A random sample of 20 adults 50 and older has been selected. Use the Poisson distribution to approximate the binomial distribution to determine the probability that no adults from this sample have had a total knee replacement.
A)0.1726
B)0.2365
C)0.3906
D)0.1004

Question

Quizplus · Accepted Answer

The Poisson distribution can be used to approximate the binomial distribution when n is large and p is small. Here, λ = np = 20 * 0.047 = 0.94. The probability of no adults having had a knee replacement is given by P(X=0) = e^(-λ) * λ^0 / 0! = e^(-0.94) ≈ 0.3906.