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.

Question

Accepted Answer

# 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
$$
\begin{align*}
n&=\frac{(1.96)^{2}\times0.54\times(1 - 0.54)}{(0.05)^{2}}\
&=\frac{3.8416\times0.54\times0.46}{0.0025}\
&=\frac{3.8416\times0.2484}{0.0025}\
&=\frac{0.95425344}{0.0025}\
& = 381.701376
\end{align*}
$$

# Answer:
$382$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for margin of error

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

Step3: Substitute the values into the formula

Answer: