Since Mr. Smith assigns grades based on actual performances of students in the class, Mr. Smith's exams have an average score of 81 and standard deviation of 12. Some do not believe Mr. Smith and have decided to take an SRS of 40 students in Mr. Smith's class and ask their exam scores.
a) What is the probability that a single student's score will be less than 73?
b) What is the probability that the average score of the sample will be greater than 80 but less than 87?