To help students improve their reading, a school district decides to implement a reading program. It is to be administered to the bottom $15\%$ of the students in the district, based on the scores on a reading achievement exam. If the average score for the students in the district is $122\mathrm{.}6,$ and it is assumed that the scores follow a normal distribution.

a$)$ Find the cutoff score that will make a student eligible for the program.

b$)$ What percent of students is expected to have a score above $150?$