# Continuous Random Variables

## Areas of Tails of Distributions

### Key Takeaways

- The problem of finding the number so that the probability is a specified value is solved by looking for the number in the interior of Figure 12.2 "Cumulative Normal Probability" and reading from the margins.
- The problem of finding the number so that the probability is a specified value is solved by looking for the complementary probability in the interior of Figure 12.2 "Cumulative Normal Probability" and reading from the margins.
- For a normal random variable with mean and standard deviation , the problem of finding the number so that is a specified value (or so that is a specified value ) is solved in two steps: (1) solve the corresponding problem for with the same value of , thereby obtaining the -score, , of ; (2) find using .
- The value of that cuts off a right tail of area in the standard normal distribution is denoted .