Question: The points \((X, Y)\) obtained by the students of a course in the two prelims is modeled by a bivariate normal distribution with parameters \(\mu_{X}=60, \mu_{Y}=75, \sigma_{X}=18, \sigma_{Y}=12, \rho=0.75 .\) Maximum possible

points in both the prelims are 100 .

1. If the final score consists of \(40 \%\) of prelim 1 and \(60 \%\) of prelim 2, then find the distribution of the final score.
2. If there are 300 students enrolled for the course, how many of them are expected to score more than 70 in prelim 1 ?
3. If 50 students score 70 in prelim 1 , how many of them are expected to score more than 80 in prelim $2 ?$

Price: $2.99

Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document