SOLUTION: 3- The quality assurance department for Pepsi Distributors, Inc. maintains meticulous records on the bottling line for two-liter Pepsi bottles. Records indicate that the process fo

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Question 1177703: 3- The quality assurance department for Pepsi Distributors, Inc. maintains meticulous records on the bottling line for two-liter Pepsi bottles. Records indicate that the process follows the normal probability distribution with a mean amount per bottle of 2.01 liters and a standard deviation of 0.025 liters. The foreman randomly selects 25 bottles from the bottling line and
determines that the mean amount per bottle is 2.005 liters
a. Compute the sampling error
b. Compute the standard error of the sampling distribution of sample means.
c. Compute the probability that the sample of 25 bottles would have a mean of 2.005 liters or more.
d. Suppose the foreman selects a second sample of 16 bottles and determines that the mean is 1.994 liters. Compute the probability that the sample of 16 bottles would have a mean of 1.994 liters or more.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
a. The sampling error is X-bar+-+mu+=+2.005+-+2.01+=+-0.005.

b. The standard error is given by sigma%2Fsqrt%28n%29+=+0.025%2Fsqrt%2825%29+=+0.005.

c. The z-score is Z+=+%28X-bar+-+mu%29%2F%28sigma%2Fsqrt%28n%29%29+=+%282.005+-+2.01%29%2F0.005+=+-1.
==> P%28X-bar+%3E=+2.005%29+=+P%28Z+%3E=+-1%29+=+0.841
***Even though the underlying distribution may NOT be normal, we know that by the CLT the distribution of the sample means is
approximately normal whose standard deviation can be known from the standard deviation of the underlying population.

d. I leave this part up to you.