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 1177652: 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.
You can put this solution on YOUR website! The SEM is s/sqrt(n)=0.025/sqrt(25)=0.005 liters. It is the sd/sqrt(n)
The sampling error is 1.96*0.005 liters or 0.0098 liters, assuming one wants to be 95% confident. The sampling error depends upon the degree of confidence; the SEM is fixed.
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z > (xbar-mean)/sigma/sqrt(n)=-0.005*5/0.025=-1, and z > -1 is 0.8413 probability
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z > (xbar-mean(/sigma/4=-0.016*4/0.025=-2.56 and z> -2.56 is 0.9948 probability
One might want to compute the probability that a sample of 16 would have a value of 1.994 or below, which is 0.0052 or very unlikely.
