The sat scores have an average of 1200 with a standard deviation of 120. 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.
Accepted Solution
A:
We first standardise [tex]\bar{x}[/tex]: P(1224 > [tex]\bar{x}[/tex])=P([tex] \frac{1224-1200}{\frac{120}{ \sqrt{36} }}[/tex]>[tex]\frac{\bar{x}-1200}{\frac{120}{\sqrt{36}}}[/tex]) which reduces to finding P(Z > 1.2) = 0.115