Question

7.4. A population of values has a normal distribution with μ-: 60.2 and σ You intend to draw a random sample of size n 129. What is the mean of the distribution of sample means? What is the standard deviation of the distribution of sample means? Round to 4 decimal places. Points possible: 5 This is attempt 1 of 5. icense

Answer 1

Let X be the random variable having normal distribution with mean $\mu=60.2$ and standard deviation $\sigma=7.4$.

Let $\bar{X}$ be the sample mean of a random sample of size n=129, drawn from this population.

Using the central limit theorem, we know that $\bar{X}$ has a normal distribution with mean

$\mu_{\bar{x}}=\mu=60.2$

and standard error (or the standard deviation of $\bar{X}$) is

$\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}=\frac{7.4}{\sqrt{129}}=0.6515$

ans: the mean of the distribution of sample means is $\mu_{\bar{x}}=60.2$

ans: The standard deviation of the distribution of sample means is $\sigma_{\bar{x}}=0.6515$