Answer:
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 <em>λ</em>, can be approximated by the Normal distribution, when <em>λ</em> is large say <em>λ</em> > 1,000.
If <em>X</em> follows Poisson (<em>λ</em>) and <em>λ</em> > 1,000 then the distribution of <em>X</em> can be approximated but he Normal distribution.
The mean of the approximated distribution of X is:
<em>μ </em>=<em> λ
</em>
The standard deviation of the approximated distribution of X is:
<em>σ </em>= √<em>λ
</em>
Thus, if λ > 1,000, then .
Let <em>X</em> = number of asbestos particles in a sample of 1 squared centimetre of dust.
The random variable <em>X</em> follows a Poisson distribution with mean, <em>μ </em>= 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 <em>z</em>-table for the probability.
Thus, the probability that 10 squared centimetres of dust contains more than 10150 particles is 0.067.