Using a binomial model estimate the sample size n such that

Using a binomial model, estimate the sample size n such that the probability of seeing one outlier is at least 90%

Solution

Given that the model is binomial we have to calculate sample size n.

And probability of seeing one outlier is at least 90% = 0.9

The formula for sample size n is,

n = p*(1-p) [z_c / E]²

we have not given critical level so we can take it as 95%.

at 95% z_c is 1.96 and assume that error E is 0.03.

= 0.9*(1-0.9) [ 1.96 / 0.03 ]²

n =384.16

Which is approximately equal to 385.