1. ## [SOLVED]Binomial Distribution Question

Hi,

I have this question.

Suppose you purchase 50,000 electrical switches and the supplier guarantees that the shipment will contain no more than 0.1% defectives. To check the shipment, you randomly sample 500 switches, test them, and find that 4 are defective. Assuming the supplier’s claim is true, compute the mean and the standard deviation for the number of defectives in a sample of 500 switches. If the supplier’s claim is true, is it likely that you have found 4 defective switches in the sample? Based on this sample, what inference would you make concerning the supplier’s guarantee?
I have been able to get this:
mean = 0.5
standard deviation = 0.7067
However, i got stuck at this part:
If the supplier’s claim is true, is it likely that you have found 4 defective switches in the sample?
How do I prove it? Need help.

Best Regards,

tommy

2. Assume the supplier's claim is true, that it contains <0.1% defective components. Then you can model the sample of 500 as independant trials of the Binomial model. So, where X is "The Number of Faulty Components":

$X = Bin(500, 0.1)$

So find the possibility that $X \geq 4$. It goes without saying that you'll have to be making a poisson substitution here.

3. if let say, i get P(X <= 4) = 0.0017 which is higher than ke one specified by the suppliers. does this mean the supplier's claim is probably not correct?

4. Originally Posted by tommyhakinen
if let say, i get P(X <= 4) = 0.0017 which is higher than ke one specified by the suppliers. does this mean the supplier's claim is probably not correct?
Assuming your working is correct, the probability (assuming that the manufacturers claim is correct) that you find 4 or fewer faulty components is 0.17%. That's unlikely enough for me, and it indicates your supplier is a lying git, and that the shipment of 50,000 will much likely contain much more than 0.1% defective components.

5. i see. now it's clear. thanks a lot.

6. hi, i think i was doing it wrongly the other day. it should be P(X>= 4) = 0.0017. this looks like not right to me. first, why in the first place we have to find P(X>=4). the question was asking is it likely that we have found 4 defective switches in the sample. can you explain to me why we first have to find P(X>=4). why not P(X<=4)?