# If 100 SAT scores are randomly selected, find the probablity that they have a mean less than 1500.Assume that SAT scores are normally distributed with mean of 1518 and standard deviation of 325.

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### 1 Answer

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.**