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
.