Question

In a Poisson distribution, μ = .38 (Round your answers to 4 decimal places.) (a)What is the probability that x=1 ? Probability= (b)What is the probability that x>3 ? Probability=

Answer 1

SOLUTION:

Recall the poisson probability formula:

$p(x)=\frac{\mu^xe^{-\mu}}{x!}$

It is given that:

$\mu=0.38$

When x=1, it follows:

$\begin{gathered} p(1)=\frac{(0.38)^1e^{-0.38}}{1!} \\ P(1)=0.2599 \end{gathered}$

For x>3:

$P(x>3)=1-P(x\le3)$

This gives:

$\begin{gathered} P(x>3)=1-(\frac{0.38^0e^{-0.38)}}{0!}+\frac{0.38^1e^{-0.38}}{1!}+\frac{0.38^2e^{-0.38}}{2!}+\frac{0.38^3e^{-0.38}}{3!}) \\ P(x>3)=0.000642 \end{gathered}$