You are now working at a carnival in charge of a "guess the bean" game. You have a huge bag of beans and people pay $1 to guess the percent of beans that are pintos; they get to take one scoop of beans and look at their sample to help them guess. If they guess within 5% of the true percentage then they win $2; if they fail to guess within 5% of the true percentage then they win nothing.

What proportion of contestants will win? Justify your reasoning.

Question

You are now working at a carnival in charge of a "guess the bean" game. You have a huge bag of beans and people pay $1 to guess the percent of beans that are pintos; they get to take one scoop of beans and look at their sample to help them guess. If they guess within 5% of the true percentage then they win $2; if they fail to guess within 5% of the true percentage then they win nothing.

What proportion of contestants will win? Justify your reasoning.

anonymous · Answer

Hmmm, so I suppose we assume that they guess will just be whatever their sample size was.

anonymous · Answer

So the real question is what is the chance that the sample size is within 5% of the actual percentage.

anonymous · Answer

First question is, what sort of probability distribution are we talking about... is it a normal distribution?

anonymous · Answer

Another way to think about this is just suppose that the sample size is 20 beans.  This means they can be off by 1 bean.

anonymous · Answer

would i use $$x+\mu+z$$ to find this?

anonymous · Answer

You don't really know what the mean is.

anonymous · Answer

I'm assuming the answer would be in terms of the mean.

anonymous · Answer

Am i supposed to make up a sample?