Need help with two problems involving Poisson Distribution

#1
Let me clarify something first. I already know the answers. What I need to know are the steps I need to take. The first one I couldn't solve myself. I've solved the 2nd one before so its probably easier than sin, but now I have no clue.

1. Last year, a manufacturer produced 300,000 DVD players. Of these, approximately 1% were defective. Assume that a simple random sample of n = 150 players is drawn. Use the Poisson approximation to the binomial distribution to compute the standard deviation of the number of DVD players that were defective.
1
1.5
50.2
1.2 (correct answer):tup:

2. Last year, a manufacturer produced 450,000 DVD players. Of these, approximately 4% were defective. Assume that a simple random sample of n = 170 players is drawn. Use the Poisson approximation to the binomial distribution to compute the probability that exactly fourteen of the 170 DVD players were defective.

0.0058 (correct):tup:
0.0119
 

Dason

Ambassador to the humans
#2
Hi! :welcome: We are glad that you posted here! This looks like a homework question though. Our homework help policy can be found here. We mainly just want to see what you have tried so far and that you have put some effort into the problem. I would also suggest checking out this thread for some guidelines on smart posting behavior that can help you get answers that are better much more quickly.
 
#4
There are straight forward formulas for both of these problems. Have you read about the Poisson distribution?
Yes.

P(x; μ) = (e-μ) (μx) / x!

Also in case it matters for a binomial distribution....
Mean: μ=n+p
Variance:σ2=n * p *q
standard deviation:σ2=n * p *q

My problem is that I don't know apply the formula(s). I'm not sure if i should follow any rules I learned with binomial distribution or if I should just ignore them either. I'm just so completely lost that I can't move on. Its probably very simple. I know I was at least able to get the answer to number 2 before and many like them, but know I just can't. I can't find any problems like this in my book or on the internet. I admit I'm not a smart person and if a question is asked in a different way then I'm used to, I have difficulties.
 
#5
Keep in mind, we have to use Poisson to approximate the Binomial. For the Poisson distribution, the mean and variance are the same.

\(\mu= \lambda= np\)
\(\sigma^2= \lambda= np\) *

The first question is asking for standard deviation. Figure out how to use * to get the answer. For the second question, we use the probability formula for Poisson. Think a little bit about what \(\mu\) equals. There is only one option. What does \(X\) equal? There is only one option.
 
Last edited: