Professor earns average $ \text{\$} 65,500$ per year with standard deviation of $\text{\$}3,500$.
Random sample of $64$.
a. Describe sampling distribution of sample mean $\bar{x}$ of average salary of these professors.
Since sample mean is the same as population mean, I said it is unbiased, since its mean is true to its parameter.
b. within what limit would you expect sample mean to fall with probability $0.95$
I used $1.96\text{SE} = 1.96\times 3,500/\sqrt{65}$ = $857.5$
therefore $95\text{% }$to fall within $\pm 857.5$ of the mean
c. obtain probability that $\bar{x}$ is greater than $66,000$
I used $(66,000 - 65,500) / 3,500 = 0.1428$ and gotten $Z$ value of $0.5557$
$1-0.5557 = 0.4443$
therefore $0.4443$ chance that $\bar{x}$ is greater than $66,000$
Can anyone shed some light if I have gotten these questions correctly.
Much appreciated!