Question 8 | BetaMath

Question 8

A local council is proposing to ban dog-walking on the beach. It is known that the proportion of households that have a dog is $\displaystyle \frac7{12}$ .

The local council wishes to poll $n$ households about this proposal.

Let $\hat{p}$ be the random variable representing the proportion of households polled that have a dog.

What is the smallest sample size, $n$ , for which the standard deviation of $\hat{p}$ is less than $0.06$ ?

A. 67

B. 68

C. 94

D. 95

Solution

If we take $n$ samples from a binomial distribution with probability of success $p$ , then the variance in the number of successes from this sample is given by the equation $\sigma^2 = np(1-p)$

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