Chapter 11.5, Problem 4Q

Suppose that the random variables $X$ and $Y$ have a bivariate normal pdf with ${\mu }_X=56$, ${\mu }_Y=11,{\sigma }_X^2=1.2,{\sigma }_Y^2=2.6$, and $\rho =0.6$. Compute $P\left(10<Y<10.5|x=55\right)$. Suppose that $n=4$ values were to be observed with $x$ fixed at 55. Find $P\left(10.5<\bar{Y}<11|x=55\right)$.