Question

suppose that you have seen the results of a poll stating that 54% of children do not know how to swim when they first go to school. for the poll to have a margin of error of 5%, how many children should be polled? round up to the nearest whole number, if necessary. in order to have a margin of error of 5%, children should be polled.

Explanation:

Step1: Recall the formula for margin of error

The formula for margin of error \(E\) in a proportion is \(E = z\sqrt{\frac{p(1 - p)}{n}}\). For a \(95\%\) confidence level (common in polls), \(z\approx1.96\). We can re - arrange the formula for \(n\): \(n=\frac{z^{2}p(1 - p)}{E^{2}}\).

Step2: Identify the values of \(p\), \(E\) and \(z\)

Given \(p = 0.54\) (proportion of children who do not know how to swim), \(E=0.05\) (margin of error), and \(z = 1.96\).

Step3: Substitute the values into the formula

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Answer:

\(382\)