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 10150 particles? Use normal approximation without continuity correction. Round your answer to 3 decimal places. Enter your answer in accordance to the question statement

The probability that 10 squared centimetres of dust contains more than 10150 particles is 0.067.

Step-by-step explanation:

The Poisson distribution with parameter λ, can be approximated by the Normal distribution, when λ is large say λ > 1,000.

If X follows Poisson (λ) and λ > 1,000 then the distribution of X can be approximated but he Normal distribution.

The mean of the approximated distribution of X is:

μ = λ

The standard deviation of the approximated distribution of X is:

σ = √λ

Thus, if λ > 1,000, then .

Let X = number of asbestos particles in a sample of 1 squared centimetre of dust.

The random variable X follows a Poisson distribution with mean, μ = 1000.

Then the average number of asbestos particles in a sample of 10 squared centimetre of dust will be, .

Compute the probability that 10 squared centimetres of dust contains more than 10150 particles as follows:

*Use a z-table for the probability.

Thus, the probability that 10 squared centimetres of dust contains more than 10150 particles is 0.067.

answer: the equation matches the regression

step-by-step explanation: