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.)
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 = 35
(c) as the sample size n increases, what happens to the standard error of the mean?
a. the standard error of the mean increases
b. the standard error of the mean decreases.
c. the standard error of the mean remains the same.
(d) if the standard deviation of a random variable x is 20 and a random sample of size n = 19 is obtained, what is the standard deviation of the sampling distribution of the sample mean?
σₓ = (type an exact answer, using radicals as needed.)

Explanation:

Step1: Recall the formula for the standard deviation of the sampling distribution of the sample mean

The formula is \(\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}\), where \(\sigma\) is the population standard deviation and \(n\) is the sample size.

Step2: Substitute the given values into the formula

Given \(\sigma = 20\) and \(n = 19\), we have \(\sigma_{\bar{x}}=\frac{20}{\sqrt{19}}\).

Answer:

\(\frac{20}{\sqrt{19}}\)