S1 help - distribution of a random variable

Ok, I am going to resit statistics in January (no!) and I was going through an exam and I have absolutely no idea how to even approach this question. As you can tell, the teacher I had for statistics was just great. :rolleyes:

4) iii) The random variable Z has teh distribution B(n,0.27). Find the smalles value of n such that P(Z >= 1) > 0.95

Thank you in advance :biggrin:

Reply 1

Trangulor

P(Z >= 1) > 0.95
is the same as saying P(Z<1) < 0.05
which is the same as saying P(Z=0)<0.05

Can you work it out from here?

Reply 2

friendsfanatic

I think so, but I thought that Z couldn't be equal to 0. My text book says: " nCx (p^x)(q^x-n), where x= 1, 2, 3 ..."

Reply 3

friendsfanatic

Is this right?:

P(Z=0) < 0.05
nC0 x 0.27^0 x 0.73^n < 0.05
0.73^n < 0.05
nlog.73 < log0.05
n> 9.52 (3 SF)

Reply 4

Trangulor

Z can equal zero, thats when none of the events give a positive

And yes, you are correct.

Perhaps to make this question easier to understand, remember that P(Z=0) =

(P(negative result))^n

P(negative result) = 0.73, that's 1-0.27

So try

0.73^n

for increasing values of n until you get something less than 0.05. This value is 10, which agrees with your answer of n>9.52 (remember that n must be a whole number)

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S1 help - distribution of a random variable

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