According to the Deloitte EV Survey, 5% of respondents indicated that they would be willing to pay an extra $500 or more for an electric vehicle versus one with a gasoline engine. A random sample of 25 adults has been selected. Use the Poisson distribution to approximate the binomial distribution to determine the probability that three or four adults from this sample would be willing to pay an extra $500 or more for an electric vehicle versus one with a gasoline engine.

Question

Quizplus · Accepted Answer

The Poisson distribution can approximate the binomial distribution when the probability is small and the sample size is large. Here, λ = np = 25 * 0.05 = 1.25. The probability of exactly 3 or 4 adults is P(X=3) + P(X=4) = (e^(-1.25) * 1.25^3 / 3!) + (e^(-1.25) * 1.25^4 / 4!) = 0.1224.

According to the Deloitte EV Survey, 5% of Respondents Indicated