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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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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