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Under what circumstances will the distribution of sample means not be normal?
The distribution of sample means will not be normal when it is based on small samples (n < 30) selected from a population that is not normal.
When would the distribution of means be normally distributed?
The general rule is that if n is more than 30, then the sampling distribution of means will be approximately normal. However, if the population is already normal, then any sample size will produce a normal sampling distribution.
Is the sampling distribution of the sample mean always normal?
This distribution is always normal (as long as we have enough samples, more on this later), and this normal distribution is called the sampling distribution of the sample mean. Because the sampling distribution of the sample mean is normal, we can of course find a mean and standard deviation for the distribution,
What is the magic number for sampling distribution?
In general, we always need to be sure we’re taking enough samples, and/or that our sample sizes are large enough. In the case of the sampling distribution of the sample mean, 3 0 30 3 0 is a magic number for the number of samples we use to make a sampling distribution.
What is the mean of a normally distributed population?
A normally distributed population has mean 57.7 and standard deviation 12.1. Find the probability that a single randomly selected element X of the population is less than 45. Find the mean and standard deviation of ˉX for samples of size 16. Find the probability that the mean of a sample of size 16 drawn from this population is less than 45.
Is the sample mean always the same as the population mean?
The mean of the sampling distribution of the sample mean will always be the same as the mean of the original non-normal distribution. In other words, the sample mean is equal to the population mean.