As you go through this course (and the next one) you will find that there are MANY "standard deviations". Although they have different names and different formulas, they ARE JUST "standard deviations". Hence, they will be called "standard error", standard deviation of the mean, standard error of a score, standard error of sampling, standard error of prediction, etc. All are used exactly the same way in relation to the normal curve.
NOW, let's look at YOUR problem
n = 1000
22% born outside U.S. = 220 (expected)
p(250) born outside U.S.
our basic formula is
(score - mean) / sd = z
(250 - 220) / sd = z
NOW, as I told you (you never pay attention :) ), there are MANY "standard deviations". In this case, we wish the standard deviation of a proportion, which is sqrt (var), with variance equal to:
n p q = n p (1 - p) = 1000 x .22 x .78 = 171.6
s.d. (proportion) = sqrt (171.6) = 13.1
so, going back to our formula:
(250 - 220) / sd = z
(250 - 220) / 13.1 = z
30/13.1 = z
2.29 = z
NOW, we go to the z tables to determine the % or probability of this z value.
I get: .011
always,
tony