# Sampling Distribution question - Probability finding

Suppose it is known that 8% of males are color blind. In a random sample of 500 males, what is the approximate probability that at least 10% of them are color blind?

I am doing review for finals and i don't understand how to solve this question. Can anyone help me with this question? Answer is

0.05

But how?

• Note that for routine textbook style exercises (as might end up in an assignment or set for homework, say) we would normally apply the self-study tag. You may like to see its tag wiki. (Beyond perhaps including the tag, I think it's probably not necessary to modify your question since you have answered it yourself.) – Glen_b Jul 12 '16 at 3:46

Okay so i was able to solve it.

we know that p-hat equals 0.1 and p equals 0.08.

so basically use the formula

phat - p/ square-root [p(1-p)/n]

Get the z-score which is

1.65

find the corresponding probability from normal table which is

0.9505

and since we need atleast 10%, we need the right side of the normal table

1 - 0.9505

equals 0.05.

• I find it interesting how different the exact answer is from that given by the normal approximation (the normal approximation with continuity correction does a little better but still isn't especially close; with $np(1-p)$ so large I'd have guessed either would be pretty close - within a percent or so on relative error - in this instance). – Glen_b Jul 12 '16 at 3:50