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A made-up pollster asks 400 people one question, and each person says yes with probability 0.25…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A made-up pollster asks people one question, and each person says yes with probability , independently. Find the standard deviation of the number who say yes. Then find the standard deviation of the proportion who say yes. Give two decimal places for the first answer and four for the second.
Need a reminder? The key ideaShow
The usual range of a binomial count is . A proportion has mean and standard deviation .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The number. people.
Step 2. The proportion. , the same as .
Answer: about people and about .
What it means. The proportion who say yes is usually within about of , which is percentage points.
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