# Would you prefer that the exam distribution had deviation = 2 or 10 if on an exam with mean = 75, you obtain a score of X = 80?

embizze | High School Teacher | (Level 1) Educator Emeritus

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Consider the two cases:

(1) `mu=75,sigma=2,x=80` . Converting your score to a standard normal score gives

`z=(80-75)/2=2.5`  The probability that a random student has a score less than yours is found in the standard normal table as .9937

The area under the standard normal curve to the left of 2.5 is .9937 or your score is in the 99th percentile.

(2) `mu=75,sigma=10,x=80` . Converting to a standard normal score yields

`z=(80-75)/10=.5` The probability that a random student has a score less than yours is found in the standard normal table as .6914

The area under the standard normal curve to the left of 0.5 is .6914 or your score is in the 69th percentile.

(3) If the teacher grades on raw scores I don't really care.

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I would prefer that the standard deviation be 2 because that puts my score in the 99th percentile.

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