Problem 58A
A health plan offers dental care and vision care benefits. Let represents the total annual amount (in millions) paid in dental care benefits. Let represents the total annual amount (in millions) paid in vision care benefits.
The health plan determined that
 where follows a normal distribution with mean 0 and variance 1,
 where follows a normal distribution with mean 0 and variance 2, and
 and are independent.
Given that the total annual vision care benefits paid by the health plan exceeds 2.5 millions, what is the probability that the total annual dental care benefits paid by the health plan exceeds 2 millions?
Problem 58B
A health plan offers dental care and vision care benefits. Let represents the total annual amount (in millions) paid in dental care benefits. Let represents the total annual amount (in millions) paid in vision care benefits.
The health plan determined that
 where follows a normal distribution with mean 0 and variance 1,
 where follows a normal distribution with mean 0 and variance 1, and
 and are independent.
What is the probability that the total annual dental care benefits exceeds 3 millions and that the total annual vision care benefits exceeds 4 millions?
_____________________________________________
_____________________________________________
Answers

Answers can be found in this page.
_____________________________________________