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

Recall the poisson probability formula:

`p(x)=(\mu^xe^(-\mu))/(x!)`

It is given that:

`\mu=0.38`

When x=1, it follows:

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