Question

What is the probability of the following
1. P (0< z < 1.46)?​

Answer 1

Approximately
.

Explanation:

(This approach requires looking up values on a
-table. Calculators aren't required.)

A typical
-table lists probabilities in the form
(or equivalently,
,) where
is real number (typically greater than or equal to
.)

However, the question asks for a probability in the form
. It would be necessary to rewrite this probability for this
-table approach to work.

Let
and
denote two real numbers, with
.
would be equal to
. In this question:

.

Look up the value of
on a
-table:
.

On the other hand,
because the Gaussian distribution is symmetric.

Therefore:

.