Q: What you mean by saying random variable is approximately normally distributed?

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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.

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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.

The sum of two random variables that are normally distributed will be also be normally distributed. Use the link and check out the article. It'll save a cut and paste.

Given "n" random variables, normally distributed, and the squared values of these RV are summed, the resultant random variable is chi-squared distributed, with degrees of freedom, k = n-1. As k goes to infinity, the resulant RV becomes normally distributed. See link.

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.

YES.

The importance is that the sum of a large number of independent random variables is always approximately normally distributed as long as each random variable has the same distribution and that distribution has a finite mean and variance. The point is that it DOES NOT matter what the particular distribution is. So whatever distribution you start with, you always end up with normal.

Suppose m is the mean and s the standard deviation of a random variable, X, which is normally distributed. Then, given Z,X = m + sZ

The results of a one-way ANOVA can be considered reliable as long as the following as The results of a one-way ANOVA can be considered reliable as long as the following assumptions are met: * Response variable must be normally distributed (or approximately normally distributed). * Samples are independent. * Variances of populations are equal. * The sample is a Simple Random Sample (SRS). ANOVA is a relatively robust procedure with respect to violations of the normality assumption (Kirk, 1995) If data are ordinal, a non-parametric alternative to this test should be used - Kruskal-Wallis one-way analysis of variance. sumptions are met: * Response variable must be normally distributed (or approximately normally distributed). * Samples are independent. * Variances of populations are equal. * The sample is a Simple Random Sample (SRS). ANOVA is a relatively robust procedure with respect to violations of the normality assumption (Kirk, 1995) If data are ordinal, a non-parametric alternative to this test should be used - Kruskal-Wallis one-way analysis of variance

The value of a random variable that is uniformly distributed between 20 and 100 can be calculated by calculating the sum of numbers from 20 to 100 and dividing it by the difference between 100 and 20. The resulting mean is 58.5.