High School Competency Test.A mandatory competency test for high school seniors has a normal distribution with a mean of 250 and a standard deviation of 100.

Directions:To receive full credit, SHOW some work (compute the z value then convert to X)OR WRITE the calculator function you are using, include relevant statistical information (mean, SD, given area, lower/upper boundaries of the region). (5pts each)

a) The top 5% of students receive $500. What is the minimum score you would need to receive this award? Round to 1 decimal place.

b) The bottom 10% of students must go to summer school. What is the minimum score you would need to stay out of this group?

c) What score corresponds to the 85th percentile?Round to the nearest whole number.