00:01
This problem says a sample of n equals 16 observations is drawn from a normal population with our mean being 1060 and standard deviation from the population being 170.
00:10
We want to come up with the probability that our sampling mean is greater than 1140, less than 970, or greater than 1026.
00:19
To do that we are going to eventually use normal cdf in our calculator.
00:23
The values we need to accomplish that for normal cdf are the lower bounds and the upper bounds.
00:29
Those are going to change for all three of our problems, but the things that are going to stay the same are our mean of our sampling that we need to use and the standard deviation as well.
00:38
Our mean will stay the same for this operation as the population mean, which is 1060, but we need to adjust our standard deviation because for the sampling it will be our population standard deviation divided by square root of n.
00:51
Which would be for our case 170 divided by the square root of n or the square root of 16, which is 4.
00:58
170 divided by 4 comes out to 42 .5.
01:01
For our first scenario where we want the probability that the mean is greater than 1140, we'll start with normal cdf...