Suppose that you work for Devin’s private consulting company, Menger Education LLC. The company hosts classes training high school students in Microsoft office products in preparation for the...

Suppose that you work for Devin’s private consulting company, Menger Education LLC. The company hosts classes training high school students in Microsoft office products in preparation for the Microsoft certifications they put out. Each student pays $500 for the 2-month course, and Devin offers a guarantee that if the student doesn’t pass the certification test, then he will refund the class and pay the student back the $100 test fee (this fee was paid to Microsoft, NOT Austin, so if the student passes then they are assumed to have paid their own fee). Devin advertises that 91% of his students pass the exam.

a) Let the random variable Y be Menger Education’s gain per student. What is the expectation with regard to company profit (gain) for the certification class, per student?

b) Suppose that in 2 years, more and more students start to sign up for the certification classes. So, the passing rate for certifications will naturally decrease, say to .87. Naturally, this will have to be reflected in the price each student pays for the course. If Menger Education intends to keep an expected profit (gain) of $400 per student, what should the cost of the course be per student?