A rowing team consist of three rowers who weight 21,36 and 42 pound. Find all possible random sample with replacement of size three and compute the sample mean for each one.use them to find the sampling distribution of the sample mean. Also verify the result
Answers
Step-by-step explanation:
Total number of all possible random samples is 3^3=273
3
=27. We can see all possible random samples in the picture. Then we compute the sample mean for each one (the fourth column of the table). Mean of all sample means is equal to \approx 35.7≈35.7. Mean of the population (42, 36, 29) is the same ( \approx 35.7≈35.7) (the mean of the sampling distribution of the sample mean is always the same as the mean of the original non-normal distribution).
Central Limit Theorem tells us that even if a population distribution is non-normal, its sampling distribution of the sample mean will be normal for a large number of samples (at least 30).
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