A certain diagnostic test is indicative of problems only if a child scores in the lowest 10% of those taking the test (the 10th percentile). If the mean score is 150 with a standard deviation of 30,...

A certain diagnostic test is indicative of problems only if a child scores in the lowest 10% of those taking the test (the 10th percentile). If the mean score is 150 with a standard deviation of 30, what would be the diagnostically meaningful cutoff?

A dean must distribute salary raises to her faculty for the next year. She has decided that the mean raise is to be $2000, the standard deviation of raises is to be $400, and the distribution is to be normal.

a. The most productive 10% of the faculty will have a raise equal to or greater than $ .

b. The 5% of the faculty who have done nothing useful in years will receive no more than $ each.