Third Level Statistics Question

Pudsy33

Looking for a bit of help, this came up on a stats exam in 2010. Can anyone give me a hand?

Only 4% of people have Type AB blood.

On average, how many donors must be checked to find somebody with
Type AB blood?

To me this seems a terrible question, no reference to population size etc.

The simple answer seems to be 25, but not convinced that is right.

Anyone have any ideas?

Victor

Assuming a random* sample within the population where the 4% was determined and that blood type for person 1 is independent of blood type for person 2 then 25 is the answer on average. However, there is no guarantee that your real life result will be person number 25 - it could be the first person or the one thousandth person.

Picking a sample of one extended family would likely result in a skewed result.

Pudsy33

Victor wrote: »

Assuming a random* sample within the population where the 4% was determined and that blood type for person 1 is independent of blood type for person 2 then 25 is the answer on average. However, there is no guarantee that your real life result will be person number 25 - it could be the first person or the one thousandth person.

Picking a sample of one extended family would likely result in a skewed result.

Cheers, that was my thinking. The issue lies in the wording of the question. Is the sample of blood donors representative of the population? There are far too many assumptions to be made.

Victor

Answer the question asked, based on the information available. Add whatever qualifications you feel are necessary.

sock puppet

You would probably be expected to state that the number of donors tested until you find the first AB blood type is geometrically distributed with p=0.04. Then for a geometrically distributed random variable its expected value is 1/p.