# How to determine if it is a p^ problem or a normal distribution

I need an overview of how probability works, how to determine if it is a p^ problem or a normal distribution

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...n of 50 and a standard deviation of 10, then they scored 2 standard deviations above the mean. Converting the test scores to z scores, an X of 70 would be:

<br>z=(70-50)/2=2

<br>So, a z score of 2 means the original score was 2 standard deviations above the mean. Note that the z distribution will only be a normal distribution if the original distribution (X) is normal.

<br>Applying the formula will always produce a transformed variable with a mean of zero and a standard deviation of one. However, the shape of the distribution will not be affected by the transformation. If X is not normal then the transformed distribution will not be normal either. One important use of the standard normal distribution is for converting between scores from a normal distribution and percentile ranks. Pls refer to attachment 1

<br>Areas under portions of the standard normal distribution are shown to the right. About .68 (.34 + .34) of the distribution is between -1 and 1 while about .96 of the distribution is between -2 and 2.

<br>If the mean and standard deviation of a normal distribution are known, it is relatively easy to figure out the percentile rank of a person obtaining a specific score. To be more concrete, assume a test in Introductory Psychology is normally distributed with a mean of 80 and a standard deviation of 5. What is the percentile rank of a person who received a score of 70 on the test? Mathematical statisticians have developed ...