If 25 SAT scores are randomly selected, find the probability that they have a mean between 1550 and 1575.Assume that SAT scores are normally distributed with mean of 1518 and standard deviation of...

If 25 SAT scores are randomly selected, find the probability that they have a mean 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. 25 SAT scores are selected randomly and the probability that they have a mean between 1550 and 1575 is required.

Here, the z-score is calculated as `(x - mu)/(sigma/sqrt N)` where N is the number of scores of which the mean is being determined.

Using the values given the x-score for 1550 is `(1550 - 1518)/(325/5) = 0.49`

and for 1575 it is `(1575 - 1518)/(325/5) = 0.87`

The area between these z-scores taken from a normal distribution table is 0.8078 - 0.6879 = 0.1199

There is a 11.99% probability that the mean of the 25 SAT scores selected is between 1550 and 1575.

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