You are doing research on variations in teacher aptitude across school districts. Several different tests are used in teacher assessment. The Teacher Aptitude Test (TAT) has a mean of 500 and a standard deviation of 150. The Teacher Quality Assessment (TQA) has a mean of 100 and a standard deviation of 10. Scores on both tests are normally distributed, in the population of teachers.

a. A teacher receives a score of 450 on the TAT. What is the equivalent score on the TQA? Fill in the blank and show your work.

The equivalent score on the TQA is: ______ (show your work).

b. Teachers are rated "low quality" if their scores on the TAT are at or below the 15th percentile. What is the score cut point for "low quality" on the TAT? Fill in the blank and show your work.

The cut point for "low quality" on the TAT is _________ points.