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 three or four adults from this sample have had a total knee replacement.
A)0.0668
B)0.4219
C)0.1145
D)0.2553

Question

Quizplus · Accepted Answer

The Poisson distribution is a good approximation to the binomial distribution when the probability of success is small and the sample size is large. In this case, the probability of success is 4.7% and the sample size is 20, so the Poisson distribution is a good approximation. The probability of three or four adults from this sample having had a total knee replacement is given by the Poisson distribution with parameter lambda = 20 * 0.047 = 0.94. This probability is 0.0668.