Answer:
p=0.3446
Step-by-step explanation:
-Let Y be the random variable with parameter [tex]\lambda=1000[/tex].
-The probability mass function is given as:
[tex]f(y)=\frac{e^{-\lambda T}(\lambda T)}{y!}, \ y\geq 0[/tex]
We set T=10, and calculate the probability as
[tex]P(Y>10040)=1-P(Y\leq 10040)\\\\=1-P[\frac{Y-10000}{\sqrt{10000}}\leq \frac{10040-10000}{100}]\\\\=1-P(Y\leq 0.4)\\\\=1-0.65542\\\\=0.34458[/tex]
Hence, the probability that 10 squared centimeters of dust contains more than 10040 particles is 0.3446
