Simple statistics question.

Stuck on a simple statistics question :P 10 POINTS for help!?

• I got a take home test and i know everything except for this multiple choice question. here's the question, Parts being manufactured at a plant are supposed to weigh 40 grams. Suppose the distribution of weights has a normal distribution mean of 40 grams and a standard deviation of 2 grams. Quality control inspectors randomly select 16 parts, weight each, and then compute the sample average weight for the 16 parts. The sampling distribution is. A. exactly Normal with a mean of 40 and standard deviation 0.5 grams B. approximately Normal with mean 40 grams and standard deviation 0.5 grams. C. meaningless in this problem, since only one sample is being selected. D. undetermined since the sample size is fairly small. i this it's C but i just want to make sure :P

• Answer:

  mr. fish - Answer B is correct. The question is about the "sampling distribution". The sampling distribution is all possible samples of size 16 from the population. Also, the sampling distribution will be approximately Normal. The sampling distribution will always have a mean EQUAL TO the population mean. So, that is equal to 40 grams. The standard deviation of the sampling distribution will vary by the size of the sample. This sample is 16, so the "sampling distribution" will have a standard deviation (or more technically correct, the standard error) equal to 2 grams divided by the square root of n or 16 in this problem. Sample Standard Error = 2 grams / sqrt 16 = 1/2 gram. Hope that helps