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 = 0.0316There is 3.16% probability that the SAT score lie between 1550 and 1575.