Question 208441: An automatic machine in a plant produces lengths of unit that if is operating properly, are nomrally distributed with a mean of 127cm, and a standard deviation of 3.1
What is the probability that if 3 units are randomly selected, their average or mean length will be greater than 130cm?
How would you approach this problem?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! population mean is 127
population standard deviation is 3.1
-----
normal distribution of values about the mean is assumed.
this means that the distribution curve is bell shaped with the mean in the middle.
------
the probability that the mean of 3 units randomly selected is above 130 will be based on the area under the normal distribution curve to the right of the value of 130.
-----
before we do this, however, we have to find the standard error of the distribution of the sample means.
----
your sample size is 3 units.
the standard error of this sample size is given by the equation:
standard error = standard deviation of the population divided by the square root of the sample size.
this comes out to be:
3.1/sqrt(3) = 1.789785834
-----
your answer turns out to be:
probability of a sample size of 3 having a mean greater than or equal to 130 is .046852 assuming the population mean is 127 and the standard error of the disbritubiton of the sample means is 1.789785834.
-----
you may duplicate this yourself by going to: http://davidmlane.com/hyperstat/z_table.html and entering a mean of 127 and a standard deviation of 1.789785834 in the top graph and then selecting above and entering 130 in that space.
-----
the area under the curve to the right of the value of 130 is the probability that the value will be 130 or above given that the mean is 127 and the standard error is 1.789785834.
-----
|
|
|
