Question

Suppose that the number of asbestos particles in a sample of 1 squared centimeter of dust is a Poisson random variable with a mean of 1000. What is the probability that 10 squared centimeters of dust contains more than 10040 particles?

Answer 1

p=0.3446

Explanation:

-Let Y be the random variable with parameter
`\lambda=1000`.

-The probability mass function is given as:

`f(y)=(e^(-\lambda T)(\lambda T))/(y!), \ y\geq 0`

We set T=10, and calculate the probability as

`P(Y>10040)=1-P(Y\leq 10040)\\\\=1-P[(Y-10000)/(√(10000))\leq (10040-10000)/(100)]\\\\=1-P(Y\leq 0.4)\\\\=1-0.65542\\\\=0.34458`

Hence, the probability that 10 squared centimeters of dust contains more than 10040 particles is 0.3446