Thread: Question regarding the normal approximation to the binomial probablility distribution

Hello, I am really having trouble with this one:

Q. Data collected over a long period of time show that a particular genetic defect occurs in 1 of every 1000 children. The records of a medical clinic show x=60 children with the defect in a total of 50,000 examined. If the 50,000 were a random sample from the population of children represented by past records,What is the probability of observing a value of X eqaul to 60 or more?

Any help will be greatly appreciated,
Cheers, RaVS

Originally Posted by RaVS

Hello, I am really having trouble with this one:

Q. Data collected over a long period of time show that a particular genetic defect occurs in 1 of every 1000 children. The records of a medical clinic show x=60 children with the defect in a total of 50,000 examined. If the 50,000 were a random sample from the population of children represented by past records,What is the probability of observing a value of X eqaul to 60 or more?

Any help will be greatly appreciated,
Cheers, RaVS

Assume the normal approximation is valid then the expected number with the defect is and its SD is

CB

Thank you Captain Black, your help is greatly appreciated.

with n large and p REALLY small I would think that the Poisson limit is correct and not the normal.

Originally Posted by matheagle

with n large and p REALLY small I would think that the Poisson limit is correct and not the normal.

The condition that I use when considering the normal approximation is . In practice this means that

Depending on the time of day and wind direction this can mean anything from to , or if we are discussing very low probability events to never (low probability events that occur in certain safety analyses for example).

Actually that is not what I usually do; I always first consider the normal approximation and only if the answer using that is not blindingly clear do I resort to exact calculation (or a better approximate method), that and the desire to impress simple minds. Reality does not really support high precision probability calculations, but we don't tell the punters this.


CB