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A survey of adults found that 34% say their favorite sport is professional football. You randomly select 130 adults and ask them if their favorite sport is professional football.

a) Find the probability that at most 66 people say their favorite sport is professional football.

The steps I have taken to solve this include:

$$n=130,\quad p=.34,\quad q=.66$$

$$\text{mean} = np = 44.2;\quad \text{standard deviation} = \sqrt{ npq} = 5.4$$ So $$z ={ 66 - 44.2 \over 5.4} = 4.03.$$

This z-score is too high to use on my chart. I don't know where to go from here.

The next question I have is how I would find the probability that MORE than 31 people say their favorite sport is professional football. I know I am doing something wrong, can anyone help? Thank you!

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    Try the probability calculator at [this site](http://www.analyzemath.com/statistics/normal_calculator.html)2011-12-21
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    In short, if the $z$-score $z$ is "off the chart, then say $P[Z\ge z]=0$ and $P[Z\le z]=1$ (you are approximating after all). And this brings up a pet peeve of mine: problems that ask you find a quantity (implying they want it exactly) that presume you will approximate the answer using the Central Limit Theorem.2011-12-21

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