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Statistics 2 Normal and Binomial Distribution

A manufacturer of spice jars knows that 8% of the jars produced are defective.
He supplies jars in cartons containing 12 jars. He supplies cartons of jars in crates o 60 cartons.
In each case make clear the distribution you are using, calculate the probability that;
1. a carton contains exactly 2 defective jars
2. a carton contains at least 1 defective jar
3. a crate contains between 39 and 44 inclusive cartons with at least 1 defective jar.
I tried to make the first one binomial but it wasn't valid?
Original post by KSmith15

I tried to make the first one binomial but it wasn't valid?


What do you mean it wasn't valid?
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KSmith15
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nq wasn't >5
Original post by KSmith15
nq wasn't >5


Binomial doesn't require nq > 5. It works for all values of n,p.

It's only the approximations that have such restrictions, and then only as approximations.
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KSmith15
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Will someone please help me to work this out?
Original post by KSmith15
Will someone please help me to work this out?


First one is a Bin(12, 0.08) distribution (counting defectives as "successes").
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Can anyone help me with the third part?
Original post by KSmith15
Can anyone help me with the third part?


You know how many are in a crate...
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I have B(60, 0.632) But how do I work out P(39<=x<=44)???
Original post by KSmith15
I have B(60, 0.632) But how do I work out P(39<=x<=44)???


P(39≤x≤44) = P(x≤44) - P(x≤38)
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KSmith15
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I can't remember how to do this, as you can't us the tables
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KSmith15
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???? Anyone, please
Original post by KSmith15
I can't remember how to do this, as you can't us the tables


You know the formula for P(X=x)... nCx*p^x*(1-p)^(n-x)?
Original post by KSmith15
I can't remember how to do this, as you can't us the tables


Looking more closely at the question, because n>30 you can use the Central Limit Theorem (don't forget it applies to every distribution).

Don't do the long-hand binomial working, or you'll be here all day!

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