A professor of physics noticed that individual students’ exam grades in his introductory course ...

1. A professor of physics noticed that individual students’ exam grades in his introductory course in physics taught in the morning historically are normally distributed. The class being taught in the morning has an average of 79 and a standard deviation of 9.5. There are 16 students enrolled in the morning class this semester. Individual exam grades in the evening class historically are also normally distributed. The evening class has an average of 75.5 with the standard deviation of 12. There are 25 students enrolled in the evening class. 

a) During the semester every class takes several exams. After every exam professor calculates the class average grade on this exam. What is the distribution of class average grades for different exams (i.e. exam 1 average, exam 2 average, etc.) for the morning session? Specify the distribution type (i.e. binomial, normal, standard normal) and its parameters (i.e. mean and standard deviation). 

What is the distribution of class average grades for different exams (i.e. exam 1 average, exam 2 average, etc.) for the evening session? Again, specify the distribution and its parameters. 

b) What is the chance that in the morning section the class average grade on the next exam will be B- (i.e. anywhere between 80 to 83)? 

c) What is the probability that in the evening section the class average on the next exam will be C- or below (i.e. lower than 73.0)? 

d) What is the probability that on the next exam the evening section will score on average higher than the morning section? To receive credit for this question, provide as much details as possible. HINT: you need to find the distribution of (evening class average exam grade MINUS morning class average exam grade).