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Statistics - Binomial Distribution Help Needed

Hi i'm doing S1 and there is one thing that i don't seem to get.
If i'm trying to find P(6<x<12) for example where B(50,0.15)

I know i need to find the probability that x<12 but i don't understand why you don't do x>6.
In the answers for AQA S1 June 2010 it says i must use 1-p(x less than or equal to 6) and i don't know why.

If someone could tell me how to do this type of question and why i'm getting it wrong it would help a lot.
Thanks
Reply 1
Original post by JamestheYorks
Hi i'm doing S1 and there is one thing that i don't seem to get.
If i'm trying to find P(6<x<12) for example where B(50,0.15)

I know i need to find the probability that x<12 but i don't understand why you don't do x>6.
In the answers for AQA S1 June 2010 it says i must use 1-p(x less than or equal to 6) and i don't know why.

If someone could tell me how to do this type of question and why i'm getting it wrong it would help a lot.
Thanks


P(6<x<12) = P(X=7,8,9,10,11)

thus

P(6<x<12) = P(7<=x<=11)... so we can use cumulative tables ... = P(<=11) - P(X<=6)
If P(7<=x) why do i have to find P(x<=6)?
Reply 3
Original post by JamestheYorks
If P(7<=x) why do i have to find P(x<=6)?


P(7<=x<=11)=P(X=7)+P(X=8)+P(X=9)+P(X=10)+P(X=11)

So we take the cumulative probabilities up to 11 and subtract the cumulative probabilities up to 6.
Ah ok i get it now thanks!

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