A state administered standardized reading exam is given to eighth grade students. The scores on this exam for all students statewide have a normal distribution with a mean of 538 and a standard deviation of 30. A local Junior High principal has decided to give an award to any student who scores in the top 15% of statewide scores. How high should a student score be to win this award? Round your answer up to the next integer.

I got 569. Can you help me checking?

mu = 538

sigma = 30

Top 15% = 85th percentile = P(X > x) = 0.15, P(X <= x) = 0.85.

From z-table, 1.04 = 0.85.

From Z = (x - mu) / sigma

We can derive that

Z * sigma = x - mu

x = mu + z * sigma

x = 538 + (1.04) (30)

x = 569.2