# Sampling and X-bar Distribution

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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!

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This solution discusses X-bar distribution and sampling in over 200 words.

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Probability

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I am a college graduate and am reviewing statistics for an upcoming test. I had a question on the following:

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 ...

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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