A mandatory competency test for high school sophomores has a normal distribution with a mean of 495 and a standard deviation of 83. Round the final answers to the nearest whole number and intermediate z-value calculations to 2 decimal places. (a) The top 2% of students receive $500. What is the minimum score you would need to receive this award? The minimum score needed to receive the award is.
(b) The bottom 3% of students must go to summer school. What is the minimum score you would need to stay out of this group The minimum score needed to stay out of this group is .