Question

complete parts (a) through (d) for the sampling distribution of the sample mean shown in the accompanying graph
click the icon to view the graph
(a) what is the value of \\( \mu _ { \overline { x } } \\) ?
the value of \\( \mu _ { \overline { x } } \\) is
sampling distribution
the distribution is normal. the locations of the
peak and inflection points are shown.

Explanation:

Step1: Recall the property of the sampling distribution of the sample mean

The mean of the sampling distribution of the sample mean \(\mu_{\bar{x}}\) is equal to the population mean \(\mu\). In a normal sampling distribution of the sample mean, the peak of the curve represents the mean of the sampling distribution.

Step2: Identify the peak value from the graph

Looking at the graph of the sampling distribution (which is normal), the value at the peak (the highest point of the curve) gives the value of \(\mu_{\bar{x}}\). From the graph, the peak is at \(x = 400\).

Answer:

\(400\)