(show work) a mandatory competency test for high school sophomores has a normal distribution with a mean of 400 and standard deviation of 100(a) the top 1.6% of the students receive $500. what is the...

(show work) a mandatory competency test for high school sophomores has a normal distribution with a mean of 400 and standard deviation of 100(a) the top 1.6% of the students receive $500. what is the minimum score you would need to receive this award? (b) The bottom 3% of the students must go to summer school. what is the minimum score you would need to stay out of this group?