Thread: binomial distributions and limit theorems!!!

find th smallest value of n in a binomial distribution for which we can assert:
P{ |(Xn/n) – p| < .1} ≥ .9

Originally Posted by lauren2988

find th smallest value of n in a binomial distribution for which we can assert:
P{ |(Xn/n) – p| < .1} ≥ .9

Well this translates into: find the smallest such that:



where the rv the number of successes in independent trials with probability of success in a single trial of . Now given the title of this thread I assume we are supposed to use a normal approximation to the binomial to do this, in which case we have:

.

of the probabilty mass of a normal RV is contained within standard deviations of the mean, so if we have:



which will allow you to find the smallest for which this is true.

Now you can do the case where yourself.

CB