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.

complete the steps to find the area of the trapezoid.

area of rectangle = 256   square units

area of triangle 1 = 24  square units

area of triangle 2 = 16  square units

area of triangle 3 =   96 square units

area of trapezoid = 120  square units

step-by-step explanation:

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step-by-step explanation: