24. How many shadest ment be rnodoely selected to eitimate the mese weelily emrinp of studests at coe college? We want to be 954, cenfideat that the umple mena is wifhin $$ \$ 5 $$ of the populatios messe and the popolation thanderd deriatics is lmows to be $$ \$ 63 $$. a 430 b. 610 c. 537 d. 862

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UpStudy AI · Accepted Answer

We use the formula for sample size in estimating a population mean:

$$
n = \left(\frac{z^* \sigma}{E}\right)^2
$$

where:
- $$ z^* $$ is the critical value corresponding to the confidence level,
- $$ \sigma $$ is the population standard deviation,
- $$ E $$ is the desired margin of error.

Given:
- Confidence level = 95% $$\rightarrow z^* = 1.96$$,
- $$ \sigma = 63 $$,
- $$ E = 5 $$.

Step 1: Substitute the given values into the formula:

$$
n = \left(\frac{1.96 \times 63}{5}\right)^2
$$

Step 2: Multiply $$ 1.96 $$ and $$ 63 $$:

$$
1.96 \times 63 = 123.48
$$

Step 3: Divide by $$ 5 $$:

$$
\frac{123.48}{5} = 24.696
$$

Step 4: Square the result:

$$
n = (24.696)^2 \approx 609.7
$$

Since the sample size must be a whole number, we round up to obtain:

$$
n = 610
$$

Thus, the answer is $$\textbf{610}$$.
The sample size needed is 610.

How many shadest ment be rnodoely selected to eitimate the mese weelily emrinp of studests at coe college? We want to be 954, cenfideat that the umple mena is wifhin of the populatios messe and the popolation thanderd deriatics is lmows to be .
a 430
b. 610
c. 537
d. 862

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How many shadest ment be rnodoely selected to eitimate the mese weelily emrinp of studests at coe college? We want to be 954, cenfideat that the umple mena is wifhin of the populatios messe and the popolation thanderd deriatics is lmows to be . a 430 b. 610 c. 537 d. 862