Question

consider a random variable x that is normally distributed. complete parts (a) through (d) below. (this is a reading assessment question. be certain of your answer because you only get one attempt on this question.) (a) if a random variable x is normally distributed, what will be the shape of the distribution of the sample mean? skewed right normal skewed left cannot be determined (b) if the mean of a random variable x is 30, what will be the mean of the sampling distribution of the sample mean? μₓ̄ = \square

Explanation:

Step1: Recall Sampling Distribution Mean

The mean of the sampling distribution of the sample mean (denoted as $\mu_{\bar{x}}$) is equal to the mean of the population from which the samples are drawn.

Step2: Apply the Concept

Given that the mean of the random variable \( X \) (the population mean) is 30, by the property of the sampling distribution of the sample mean, $\mu_{\bar{x}} = \mu = 30$.

Answer:

30