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Answer:
The approximate probability that 10 squared centimeters of dust contains more than 10110 particles is 0.1357
Step-by-step explanation:
For a sample of 10 sqaured centimeters of dust, the total amount of asbestos particles has a Poisson distribution with a mean of 1000/1 * 10 = 10000.
We will approximate this probability to a normal distribution. The variance is also 10000 (because it is poisson), therefore the standard deviation is √10000 = 100. Lets call X the distribution, and W its standarization, given by
We have
Where is the cummulative distribution function of a standard normal distribution. The values of
are well known and they can be found in the attached file.
We conclude that the approximate probability that 10 squared centimeters of dust contains more than 10110 particles is 0.1357.