sampling distribution question

By statistics, faculty with rank of assistant professor(AP) finishing their 2nd year of employment at a higher education institution in Ontario earn an average of $68,500 per year with a standard deviation of $3500. In an attempt to verify this salary level, a random sample of 49 AP with 2 years of experience was selected from a personnel database for all higher education institution in Ontario.

a) Describe the sampling distribution of the sample mean X bar of the average salary of these 49 AP.

b) Within what limit would you expect the sample mean to fall with probability 0.95.

c) If the random sample actually produced a sample mean of 70,000, would you consider this rather unusual? What conclusion might you draw then?

I have hard time understanding the questions, which formula do I use for these, for part a, what is decibing it mean?

Re: sampling distribution question

Quote:

Originally Posted by

**wopashui**

a) Describe the sampling distribution of the sample mean X bar of the average salary of these 49 AP.

As from your last post $\displaystyle \displaystyle \bar{x}$ is $\displaystyle \displaystyle N\left(\mu, \left(\frac{\sigma}{\sqrt{n}}\right)^2\right)$

Quote:

Originally Posted by

**wopashui**

b) Within what limit would you expect the sample mean to fall with probability 0.95.

Use the information from a) and the normal probability tables.

Quote:

Originally Posted by

**wopashui**

c) If the random sample actually produced a sample mean of 70,000, would you consider this rather unusual? What conclusion might you draw then?

Did 70,000 fall within the limits found in part b)?