Question

The sat scores have an average of 1200 with a standard deviation of 60. a sample of 36 scores is selected. what is the probability that the sample mean will be larger than 1224? round your answer to three decimal places.

Answer 1

Theorem: If a random variable is normally distributed with a mean of µ and a standard deviation of σ, then the sample mean with a sample size of n would be normally distributed too with the same mean and a standard deviation of $\frac{\sigma}{ \sqrt{n} }$. 

In this case, µ = 1200,  σ = 60, sample size n = 36.
So the sample mean has a mean of 1200 and a standard deviation of $\frac{\sigma}{ \sqrt{n} }= \frac{60}{ \sqrt{36} }=10$.
Then the z-score that corresponds to 1224 is