# Plots of Poisson Distribution

When can you use the Normal distribution to approximate the Poisson distribution, assuming you have "n" independent trials each with a probability of success of "p"?

- When the mean of the Poisson distribution is very small
- When the variance of the Poisson distribution is very small
- When the number of observations is very large and the success rate is close to 1
- When the number of observations is very large and the success rate is close to 0

**C.**

The Normal distribution can approximate the distribution of a Poisson random variable with a large lambda parameter (Î»). This will be the case when both the number observations (n) is very large and the success rate (p) is close to 1 since Î» = n*p.

**INCORRECT: A,** The mean of a Poisson distribution must be large to allow approximation with a Normal distribution

**INCORRECT: B,** The variance of a Poisson distribution must be large to allow approximation with a Normal distribution

**INCORRECT: D,** The Normal distribution can approximate the distribution of a Poisson random variable with a large lambda parameter (Î»). But since Î» = n*p, where n is the number observations and p is the success rate, Î» will not be large if p is close to 0

The number of false fire alarms in a suburb of Houston averages 2.1 per day. What is the (approximate) probability that there would be 4 false alarms on 1 day?

- 1.0
- 0.1
- 0.5
- 0.0

**B.**

Use Poisson distribution

P(X = x) = [Î» x *e-Î»]/ Î»!

Is there any other intuitive way as well???