Sampling and X-bar Distribution
A Company produces candy on a production line. When operating properly, the production process will produce an average of u=140 pounds of candy per hour with a standard deviation of o=20 pounds of candy per hour. It is also known that the distribution is skewed left. In order to monitor the assembly process, 100 hours are randomly sampled and the number of pounds of candy produced is recorded. The sample mean number produced x-bar will be used to determine whether the production operation is working correctly.
-Can you explain to me how the sampling distribution of x-bar is generated theoretically and what would be the property(ies) of this x-bar distribution when the production is working properly?
-If the sample mean of the x-bar is 70 for the 100 hours…does this mean that the assembly is producing too few pounds of candy on average?
Thank you very much!