Check my answers/method please. c:
Q. The number of breakdowns per week experienced by a certain type of machine can be assumed to follow a Poisson distribution with mean 0.5. There are five of these machines in a workshop.
a. Find the probability that, during a randomly chosen week, there is a total of 2 breakdowns on all these machines.
b. Use an appropriate approximation to find the probability that, during a period of 50 weeks, the total number of breakdowns on these machines is less than 100.

Question

Check my answers/method please. c: 
Q. The number of breakdowns per week experienced by a certain type of machine can be assumed to follow a Poisson distribution with mean 0.5. There are five of these machines in a workshop. 
a. Find the probability that, during a randomly chosen week, there is a total of 2 breakdowns on all these machines. 
b. Use an appropriate approximation to find the probability that, during a period of 50 weeks, the total number of breakdowns on these machines is less than 100.

loinducoeur · Answer

A. a. 5X ~ Po(2.5) => P(5X = 2) = $$\frac{ e ^{-2.5} \times2.5^{2} }{ 2! } = 0.2565$$ to 4 d.p.

b. Am I supposed to use the Central Limit Theorem here after approximating to the Normal distribution?? Or is it the case of, approximating to the Normal distribution & standardising as usual?

loinducoeur · Answer

Doesn't matter. It's the usual standardisation. Thanks a bunch, guys(!) You're so great at helping people(!) You're so especially good at Stats too(!)