Exactly "what it says on the tin"! The distribution is nearly, but not quite, the standard normal, or Gaussiam distribution.
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The answer depends on how the sample is selected. If it is a simple random sample, of size n, then it is distributed approximately normally with the same mean as the population mean.The answer depends on how the sample is selected. If it is a simple random sample, of size n, then it is distributed approximately normally with the same mean as the population mean.The answer depends on how the sample is selected. If it is a simple random sample, of size n, then it is distributed approximately normally with the same mean as the population mean.The answer depends on how the sample is selected. If it is a simple random sample, of size n, then it is distributed approximately normally with the same mean as the population mean.
Yes, to approximately standard normal.If the random variable X is approximately normal with mean m and standard deviation s, then(X - m)/sis approximately standard normal.
If a normally distributed random variable X has mean m and standard deviation s, then z = (X - m)/s
According to the Central Limit Theorem, even if a variable has an underlying distribution which is not Normal, the means of random samples from the population will be normally distributed with the population mean as its mean.
It means that the random variable of interest is Normally distributed and so the t-distribution is an appropriate distribution for the test rather than just an approximation.