Binomial distribution: Find smallest integer such that....

[Josephine]

The results of an experiment show that the discrete random variable X has a binomial probability distribution with mean 1.2 and variance 1.18. Calculate P(X=1) and find the smallest integer r such that P(X>r) > 0.85

I've found P(X=1), which is 0.364, but I'm not sure about getting the smallest integer r.

P(X>r) > 0.85
1 - P(X<=r) > 0.85
P(X<=r) < 0.15
..........

 

[JakeD]

Re: Binomial distribution: Find smallest integer such that..

The results of an experiment show that the discrete random variable X has a binomial probability distribution with mean 1.2 and variance 1.18. Calculate P(X=1) and find the smallest integer r such that P(X>r) > 0.85

I've found P(X=1), which is 0.364, but I'm not sure about getting the smallest integer r.

P(X>r) > 0.85
1 - P(X<=r) > 0.85
P(X<=r) < 0.15
..........

There is something wrong with the question. You know P(X<=1) > .15. Calculate P(X=0) and find P(X<=0) > .15 too. So r can only be negative. But there is no smallest negative integer. Hmm...

 

[Josephine]

Mistake

Oh I'm so sorry, I made a typing mistake. It is actually P(X<r)>0.85

 

[JakeD]

Re: Mistake

Oh I'm so sorry, I made a typing mistake. It is actually P(X<r)>0.85

OK, so calculate P(X=i) for i = 0, 1, 2 etc until you get the sum of those probabilities > .85.