I have the answer in the back of my book to this problem, but could not comprehend how they came up with this answer, any clarification is highly appreciated:

local newspaper polls 400 voters in an attempt to predict whether the budget will pass. suppose that the badget actually has the support of 52% of the voters. what is the probability the newspapers's sample will lead them to predict defeat?

their answer was 0.212

i wonder how is the probability that i need tocalculate: is it the 48% who do not support the budget?


What the answer is working with is a random variable X~Binomial(400,0.52) and you have to work out the probability that X is less than 200 (or predicting that less than 50% will support it during the poll).

You will need to use the Central Limit Theorem to do this, you're tables will not provide the answer.

Give it a try and let me know if you have any problems,