Answer:
a) a. Normal
b) The mean of the sampling distribution of the sample mean is 40.
c) C. The standard error of the mean decreases.
d) The standard deviation of the sampling distribution of the sample mean is 2.58.
Step-by-step explanation:
(a) If a random variable X is normally distributed, what will be the shape of the distribution of the sample mean?
If the variable is normally distributed, then the sample mean is going to be normally distributed. So the correct answer is
a. Normal
(b) If the mean of a random variable X is 40, what will be the mean of the sampling distribution of the sample mean?
The mean of the sampling distribuion is the same, so it is 40.
(c) As the sample size n increases, what happens to the standard error of the mean?
We have that:
In which is the standard deviation. So, as the sample size n increases, the standard error of the mean decreases. The correct answer is
C. The standard error of the mean decreases.
(d) If the standard deviation of a random variable X is 10 and a random sample of size nequals15 is obtained, what is the standard deviation of the sampling distribution of the sample mean
We have that:
The standard deviation of the sampling distribution of the sample mean is 2.58.