1. ## Rare events

The ethnicity of about 93.5 percent of the population of Gemany is Caucasian. Suppose you will take a random sample of 473 Germans.

What proportions of Caucasians would be rare events?

how can i solve this one?

i tried msum+1.96*sigma SD, but its all wrong

2. Originally Posted by makaveli89
The ethnicity of about 93.5 percent of the population of Gemany is Caucasian. Suppose you will take a random sample of 473 Germans.

What proportions of Caucasians would be rare events?

how can i solve this one?

i tried msum+1.96*sigma SD, but its all wrong
What do you mean by "rare event"? If it is "happening with probably less that 5%", as I guess, then it is a consequence of the central limit theorem and of usual independence hypotheses that a rare event would be a proportion that differs from the mean ( $0.935$) by more than around $\frac{1.96 \sigma}{\sqrt{n}}$ where $n=473$ and $\sigma=\sqrt{0.935\times (1-0.935)}\simeq 0.247$, that is to say a proportion of Caucasians larger than about 0.958 or less than about 0.912. This correspond to about $442\pm 11$ people among 473.

I'm really surprised that this question is being asked in Germany because I could not imagine it happening in France, where some people would find this politically incorrect to distinguish people according to their "ethnicity". By the way, the law here forbids to do polls on what you call "ethnicity", or origin, and for that reason no official proportion can be given.