Homework SourseSuppose that the number of asbestos particles in a sample of
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 10120 particles?
Solution
for 10cm, the mean is 10*1000 = 10,000
we use normal approximation, => X ~ N( lambda, lambda) , where lambda = mean for 10cm = 10,000
| mean = 10000 |
| Std Dev (s) =10000 |
| Find : P( x > 10010 ) z = ( x - u )/s = ( 10010 - 10000 )/10000 = 0.001 P( x > 10010) = P( Z > 0.001) = P( Z < -0.001) = 0.4996 _ _ _ _ _ _ _ _ _ (From Z-table) = 49.96% |
