06:36
Probability with Applications in Engineering, Science, and Technology
For a Calculus I class, the final exam score $Y$ and the average $X$ of the four earlier tests have a
bivariate normal distribution with mean $\mu_{1}=73,$ standard deviation $\sigma_{1}=12,$ mean $\mu_{2}=70$ , standard deviation $\sigma_{2}=15 .$ The correlation is $\rho=.71 .$ Determine
$\begin{array}{ll}{\text {
(a) }} & {\mu_{Y|X=x}} \\ {\text {
(b) }} & {\sigma_{Y|X=x}^{2}} \\ {\text {
(c) }} & {\sigma_{Y|X=x}}\end{array}$
(d) $P(Y>90 | X=80),$ i.e., the probability that the final exam score exceeds 90 given that the average of the four earlier tests is 80