## Continuous Random Variables

First, this section talks about how to describe continuous distributions and compute related probabilities, including some basic facts about the normal distribution. Then, it covers how to compute probabilities related to any normal random variable and gives examples of using -score transformations. Finally, it defines tail probabilities and illustrates how to find them.

### 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 .