The binomial probability for P(x

Question

The binomial probability for P(x < 2), where n = 18, p = .05 is .9418.If you use the Poisson distribution to approximate this binomial probability, what probability would you produce?
A).7656
B).8146
C).9372
D).9514
E).9716

Quizplus · Accepted Answer

The Poisson distribution can be used to approximate the binomial distribution when n is large and p is small. The mean ($\lambda$) of the Poisson distribution is $n \times p$. Here, $\lambda = 18 \times 0.05 = 0.9$. The probability of $P(x < 2)$ using the Poisson distribution is the sum of the probabilities of $x = 0$ and $x = 1$, which can be calculated using the Poisson probability formula: $P(x) = \frac{e^{-\lambda} \lambda^x}{x!}$. Thus, $P(x < 2) = P(x = 0) + P(x = 1) = e^{-0.9} + 0.9e^{-0.9} = 0.9372$.

The Binomial Probability for P(x < 2), Where N =