The number that die has a binomial distribution, but here we have moderatelyOriginally Posted by Blockface
large numbers so we will use the normal approximation to the binomial distribution.
Expected number of deaths in cases is .
The standard deviation of a binomially distributed random variable is ,
where is the number of trials ( in this case), is the probability
of the outcome of interest on a single trial (in this case ). So the
standard deviation of the number of deaths is:
So now the question is: what is the probability of 35 or fewer deaths
happening by chance assuming the treatment has no effect.
We work with 35.5 or fewer to allow for the continuous nature of the normal
approximation, and so the critical z-score we are interested in is:
This is looked up in a table of the cumulative standard normal distribution to