# How to find the minimum sample size.

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A processor of carrots cuts the green top off each carrot, washes the carrots, and inserts six into a package. Twenty packages are inserted in a box for shipment. To test the weight of the boxes, a few were checked. The mean weight was 20.4 pounds, with a standard deviation of 0.5 pounds. How many boxes must the processor sample to be 95% confident that the sample mean does not differ from the population mean by more than 0.2 pounds?

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The solution contains detailed explanation of how to find the minimum sample size.

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This is a problem about the sample size. Given the standard deviation sigma=0.5, the margin of error is ME<=0.2. For a 95% confidence level, z=1.96. Hence, we can ...

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- BSc , Wuhan Univ. China
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###### 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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