Section 8.1 Homework

5. 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?

1. Skewed right
2. Normal
3. Skewed left
4. Cannot be determined

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(b) If the mean of a random variable X is 35​, what will be the mean of the sampling distribution of the sample​ mean?

​(c) As the sample size n​ increases, what happens to the standard error of the​ mean?

1. The standard error of the mean remains the same.
2. The standard error of the mean decreases.
3. The standard error of the mean increases

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(d) If the standard deviation of a random variable X is 15 and a random sample of size n=17 is​ obtained, what is the standard deviation of the sampling distribution of the sample​ mean?