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.
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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.
NO
It will be the same as the distribution of the random variable itself.
A sampling distribution function is a probability distribution function. Wikipedia gives this definition: In statistics, a sampling distribution is the probability distribution, under repeated sampling of the population, of a given statistic (a numerical quantity calculated from the data values in a sample). I would add that the sampling distribution is the theoretical pdf that would ultimately result under infinite repeated sampling. A sample is a limited set of values drawn from a population. Suppose I take 5 numbers from a population whose values are described by a pdf, and calculate their average (mean value). Now if I did this many times (let's say a million times, close enough to infinity) , I would have a relative frequency plot of the mean value which will be very close to the theoretical sampling pdf.
a large number of samples of size 50 were selected at random from a normal population with mean and variance.The mean and standard error of the sampling distribution of the sample mean were obtain 2500 and 4 respectivly.Find the mean and varince of the population?