Statistics quick! Is this right?
posted by Laura .
I need to verify one of my answers quickly...the problem is:
The mean annual salary for classroom teachers is $43,658. Assume a standard deviation of $8000.
1) Determine the sampling distribution of the sample mean for a sample of size 256. Interpret your answer in terms of the distribution of of all possible sample mean salaries for samples of 256 teachers.
2) Determine the percentage of all samples of 256 public school teachers that have mean salaries within $1000 of the population mean salary of $43,658. Interpret your answer in terms of sampling error.
Are my answers correct? :
1)SE within samples = 8,000/√256 =500
2) 42.1% of samples are within $500 of the mean $8,000.
or...
is it 84.2% that're 1/in $1000?
or...
am I way off?

1) looks correct
For 2) You have an standard error of 500, and are asked what is likelihood of similar sample being within 1000 or 2.0 standard deviations away from the mean. Look up 2.0 in your cumulative normal distribution table (probably in the back of your stats book). I get .9772  meaning 97.72% of such samples with be within $1000 of the mean of $43,658