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If 1 SAT score is randomly selected, find the probability that it is between 1550 and...

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surfer3 | Valedictorian

Posted May 26, 2012 at 3:44 AM via web

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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

Posted May 26, 2012 at 5:51 AM (Answer #1)

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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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