part 2. (6 points) normal distributions the normal distribution curve to the right displays the distribution of grades given to managers based on management performance at ford. of the large population of ford managers, 10% were given a grades, 80% were given b grades, and 10% were given c grades. a’s were given to those who scored 380 or higher and c’s were given to those who scored 160 or lower. a. (2 point) what are the z scores associated with the 10th and 90th percentiles from the standard normal distribution? recall that a z-score is value from the standard normal distribution and represents the number of standard deviations a value is away from its mean. b. (2 point) from part a, you should have two values - the z-scores associated with the 10th and 90th percentiles. using these two values and the mathematical definitions of a z-score, calculate the mean and standard deviation of the performance scores? show work. c. (2 point) suppose the company adds grades d and f so there are 5 categories to grade performance. if they want to give a’s only to those in the top 3%, what performance score must a manager exceed to get an a?