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A researcher wants to go from a normal distribution to a standard normal distribution because the latter allows him/her to make the correspondence between the area and the probability. Though events in the real world rarely follow a standard normal distribution, z-scores are convenient calculations of area that can be used with any/all normal distributions. Meaning: once a researcher has translated raw data into a standard normal distribution (z-score), he/she can then find its associated probability.

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Q: Why does a researcher want to go from a normal distribution to a standard normal distribution?

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It is any shape that you want, provided that the total area under the curve is 1.

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A normal distribution simply enables you to convert your values, which are in some measurement unit, to normal deviates. Normal deviates (i.e. z-scores) allow you to use the table of normal values to compute probabilities under the normal curve.

While the initial standard should be based on a distribution of some kind, and possibly not even the normal, each personal grade should not be based on it.

In statistics, an underlying assumption of parametric tests or analyses is that the dataset on which you want to use the test has been demonstrated to have a normal distribution. That is, estimation of the "parameters", such as mean and standard deviation, is meaningful. For instance you can calculate the standard deviation of any dataset, but it only accurately describes the distribution of values around the mean if you have a normal distribution. If you can't demonstrate that your sample is normally distributed, you have to use non-parametric tests on your dataset.

I just want to have the question answered for class

It depends on what the underlying distribution is and which coefficient you want to calculate.

Type your answer here... It depends what percentage of the total data you want to embrace. 99.73% of the total distribution lies between minus to plus 3 standard deviations. That's usually the benchmark range.

It depends on what you want to test. Goodnesss of fit or some null hypothesis?

See the related link for the area at 0.41 (same as -0.41) which is 0.1591. This area, which is the probability, is from minus infinity to -0.41. If you want the area from -0.41 to plus infinity you need to take 1 - 0.1591 which is 0.8409.

The answer is about 16% Using the z-score formula(z = (x-u)/sd) the z score is 1. This means that we want the percentage above 1 standard deviation. We know from the 68-95-99.7 rule that 68 percent of all the data fall between -1 and 1 standard deviation so there must be about 16% that falls above 1 standard deviation.

Yes, it is.

Yes, it is normal. But, it is not normal when you want to do it every single day.

(1) It shows the researcher visually the particular thing they are researching, (2)The Internet tells the researcher reality on the particular things they want to research.

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