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If 1 SAT score is randomly selceted, find the probablitity that it is less than...

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surfer3 | Valedictorian

Posted May 26, 2012 at 3:41 AM via web

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If 1 SAT score is randomly selceted, find the probablitity that it is less than 1500.

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 5:36 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 is less than 1500, find the z-score of 1500

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

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

The z-score is `(1500 - 1518)/325 = -0.0553`

Use a normal distribution table to find the corresponding area for this z-score. The value is 0.4801

There is 48.01% probability that the SAT score is less than 1500

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