Probability/stats help needed. Rep given!

Hey, I will give some rep if someone can help me by showing me how to solve a few example questions, which are below. I am looking for the method and help more than the answer, but if you can do it all, that will be well worth some reputation points :biggrin:

It's not too hard it's just Ive not got notes on how to do it, and am a bit rusty. Thanks in advance, rep awarded by tomorrow afternoon for good response.

1. 0.3% of bolts made by a machine are defective, defective bolts are produced randomly during production. If bolts are in packets of 100 bolts, what is the Poisson approximation that a random box will contain x defective bolts?

If you buy 8 packs of bolts, what is the distribution of the number of boxes that contain NO defective bolts? What is the expected number of boxes with no defectives?

2. Events occur randomly at rate r and are counted over a time period of length, s so the event count X is Poisson. When:

r = 0.01 and s = 200, find:

a) P(X=2) and b) P(X<2)

3. Suppose that X is N(-1, 4), find:
a) P(X<0) b) P([X+1]< X <1) here the square brackets mean the modulus of X+1

I can do the first wordy one mostly, just gets a little confusing and my answer is odd... but if you can help with the others I'd be very grateful.

-Rob

Reply 1

Retropmot

for poission you have only the mean parameter which is given by 0.003*100

for the next bit use a binomial distribution with the probability of having no defefects being your p which can be found from putting x = 0 into your anwser for the previous part. The expected value from the binomial distribution is np with n = 8 and p the probabilty of no defects found from the first part

question 2 is just substituting values into the poisson distribution formula. The mean is found by mulitplying the lenght of the sample by the rate so your mean is 0.01*200
for the P(x<2) just do P(X=0) + P(X=1)

Reply 2

generalebriety

X~N(-1,4)
transformation equation: Z = (X + 1) / 2
a) P(X<0) = P(Z<(0+1)/2) = P(Z<1/2) = 1 - Phi(0.5) [use tables]

b) I don't get it... I don't see when |a+1| < a for any a at all. Graph y=x and y=|x+1| and you'll see the latter is never less than the former.