# If 1 SAT score is randomly selected, find the probability that it is between 1550 and 1575.Assume that SAT scores are normally distributed with mean of 1518 and standard deviation of 325.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The SAT scores are normally distributed with a mean of 1518 and a standard deviation of 325. To determine the probability that it lies between 1550 and 1575 find the z-score for these values and use it to determine the area that lies between them from a normal distribution table.

The z-score for a value x is given by `(x - mu)/sigma`

Here `mu = 1518` and `sigma = 325`

For 1550, the z-score is `(1550 - 1518)/325 = 0.098`

and for 1575 it is `(1575 - 1518)/325 = 0.17`

The area between these values from the normal distribution table is 0.5675 - 9.5359 = 0.0316

There is 3.16% probability that the SAT score lie between 1550 and 1575.

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