00:02
In question a, we're told the population mean is $21 .50 per hour, and the standard deviation for the population is $350 an hour.
00:12
We want to figure out the mean and the standard deviation for our sample size of $150.
00:18
So the central limit theorem says if we select 150 employees at random, the average for those 150 employees should be pretty darn close to the population average, $21 .50.
00:33
And the standard deviation for our sample will be equal to the population standard deviation, $0 .50, divided by the square root of our sample size, which is 150.
00:46
And when you do 3 .5 divided by the square root of 150, we get a standard deviation of 0 .29.
01:00
Now for question b.
01:04
We want to construct a 99 % confidence interval for the mean price of all the homes in the state.
01:11
So we're going to be using this formula, and we can use z as our critical value because we know the population standard deviation.
01:19
So our sample mean was $344 ,750.
01:24
That's going to be our x -bar.
01:27
For 99 % confidence, the critical value z -star would be 2 .576.
01:34
The population standard deviation is 63 ,150, and our sample size was 1 ,500.
01:46
That's going to be our end value.
01:49
So now the first thing i'll do is use my calculator to get our margin of error, which comes out to be $4 ,200...