Question

practice e8
score: 2/10 answered: 1/5
question 2
a population has parameters \\( \mu=147.5 \\) and \\( \sigma=69.5 \\). you intend to draw a random sample of size \\( n = 32 \\).
what is the mean of the distribution of sample means?
\\( \mu_{\bar{x}}= \\)
what is the standard deviation of the distribution of sample means?
(report answer accurate to 2 decimal places.)
\\( \sigma_{\bar{x}}= \\)
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Explanation:

Step1: Find the mean of the distribution of sample means

The mean of the distribution of sample means ($\mu_{\bar{x}}$) is equal to the population mean ($\mu$).
$\mu_{\bar{x}}=\mu$
Given $\mu = 147.5$, so $\mu_{\bar{x}}=147.5$

Step2: Find the standard deviation of the distribution of sample means

The formula for the standard deviation of the distribution of sample means ($\sigma_{\bar{x}}$) is $\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$.
Given $\sigma = 69.5$ and $n = 32$.
First, calculate $\sqrt{32}\approx5.656854$.
Then $\sigma_{\bar{x}}=\frac{69.5}{5.656854}\approx12.28$

Answer:

The mean of the distribution of sample means: $147.5$
The standard deviation of the distribution of sample means: $12.28$