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 got 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 35, what will be the mean of the sampling distribution of the sample mean?
μx¯=□

Explanation:

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

If \(X\) is normally distributed, then the sampling distribution of the sample mean \(\bar{X}\) is also normally distributed. This is a fundamental property in statistics.

Step2: Recall the formula for the mean 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 \(\mu\). Given that \(\mu = 35\), we have \(\mu_{\bar{X}}=\mu\).

Answer:

a. Normal
b. \(35\)