Year 12 Methods (Unit 3 & 4)
Sampling and estimation
Approximating the distribution of the sample proportion
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Question 1
194630
A random sample of size \(n=100\) is taken from a large population in which the proportion of successes is \(p=0.5\). For large \(n\) the sample proportion \(\hat p\) is approximately normal with mean \(p\) and standard deviation \(\sqrt{\dfrac{p(1-p)}{n}}\). What is the standard deviation of \(\hat p\)?
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