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
`(\sigma)/( √(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
`(\sigma)/( √(n) )= (60)/( √(36) )=10`.
Then the z-score that corresponds to 1224 is