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As n increases the sampling distribution of pˆ (p hat) becomes approximately normal.
a) T or F The sampling distribution will be normal. Explain your answer. b) Find the mean and standard deviation of the sampling distribution. c) We pick one of our samples from the sampling distribution what is the probability that this sample has a mean that is greater than 109 ? Is this a usual or unusual event? these are the rest of the question.
Thanks to the Central Limit Theorem, the sampling distribution of the mean is Gaussian (normal) whose mean is the population mean and whose standard deviation is the sample standard error.
If the samples are drawn frm a normal population, when the population standard deviation is unknown and estimated by the sample standard deviation, the sampling distribution of the sample means follow a t-distribution.
The normal distribution is always continuous.