The SAT placement test for admission to American universities had an average of μ = 1026 and a standard deviation σ = 209. The distribution of marks is approximately normal.
a) Ramon had a grade of 1100. If the notes have a normal distribution, to what percentile does Ramon's note correspond?
b) Now consider the average X¯ of the scores of 70 randomly selected students. If X¯ = 1100, at what percentile of the sampling distribution of X¯ does this result correspond?
c) Which of your two calculations, a) or b), is less precise since SAT notes do not follow exactly a normal law?
Here is my approach:
a) I calculated z-score = 0.354 then I found that the proportion correspond is 0.6368. So what is the percentile correspond? 63.68 or 64?
b) I obtained z-score =2.96 so the proportion is 0.9985. Then what is the percentile?