binomial sample probability

Nov 2013
263
59
Australia
Twenty-percent of the residents of Boston were born outside of the United States. A random sample of 400 residents is to be selected. Without using the Z table, compute the approximate probability that at least 22% of those in the sample were born outside of the United States.

I really don't know what I am supposed to do.
Thanks in advance for your help. :)
 

Plato

MHF Helper
Aug 2006
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Twenty-percent of the residents of Boston were born outside of the United States. A random sample of 400 residents is to be selected. Without using the Z table, compute the approximate probability that at least 22% of those in the sample were born outside of the United States.
I really don't know what I am supposed to do.
Well, I do not know what you are expected to do. There are several possibilities.What topics are being currently discussed in your lecture sections and/or textbook? Surely it must have to do with approximations? Otherwise, a direct calculation would answer the question.
 
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Nov 2013
263
59
Australia
Hi Plato and thanks for answering,

I 'swipe' interesting questions off other people so I am not actually studying this at all.
The direct calculation would be very long winded wouldn't it? Working out lots of binomial probabilities and adding them all together?
I am probably just out of my depth. I like probability but I am not very familiar with these large number statistical type ones. :/