The SAT scores are normally distributed with a mean of 1518 and a standard deviation of 325. 100 SAT scores are selected randomly and the probability that they have a mean less than 1500 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 is `(1500 - 1518)/(325/10) = -0.55`
The area for a z-score of less than -0.55 is 0.2912
There is a 29.12% probability that the mean of the 100 SAT scores selected is less than 1500.