If we calculate the probability P(A) that event A will occur and obtain the corresponding confidence interval&nbsp;z1. If I have n trials, the expected number of trials that will result in event A is&nbsp;n⋅P(A). But what then is the confidence interval&nbsp;z2&nbsp;for this expected number of events A?

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If we calculate the probability P(A) that event A will occur and obtain the corresponding confidence interval&amp;nbsp;z1. If I have n trials, the expected number of trials that will result in event A is&amp;nbsp;n⋅P(A). But what then is the confidence interval&amp;nbsp;z2&amp;nbsp;for this expected number of events A?

Klanglinkmgk · Accepted Answer

Step 1If X∼B∈om(n,p),, is the number of Successes observed in n independent trials and p is the probability of Success on any one trial, then p^=Xn is the point estimate of p. A Wald 95% confidence interval (CI) for p is of the formp^±1.96p^(1−p^)n,Multiplying through by n, you would have the following 95% CI for E(X):X±1.96np^(1−p^).1) these formulas depend on a normal approximation to a binomial distribution. They work best when n is large and p is not too far from 12. A common approximate rule of thumb is that np and n(1−p) should both exceed 5.2) The Agresti CI for p is more accurate, particularly when n&amp;lt;500 or so: Define n~=n+4 and p~=p+2n~.. Then compute the CI for p as:p~±1.96p~(1−p~)n~,

If we calculate the probability P(A) that event A will occur and obtain the corresponding confidence

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