Question

Find the area under the standard normal curve to the left of z = 1.31

Answer 1

Let X be a random variable which have standard normal distribution, i.e. mean=0,
and variance=1.
Then the area under the standard normal curve over the
interval [a,b] is equal to the probability
P(X belongs to
[a,b]).

In particular, the area under the standard normal curve to the
left some value t is equal to
P(X<t)

The function F:R -> R
defined by
F(t) = P(X<z)
is called cummulative probability
distruibution and its vaules can be found in almost all books in Probability
Theory.

We should find F(1.31).
In Excel one can use the function
NORMSDIST.
Then
F(1.31) = P(X<1.31) = NORMSDIST(1.31) = 0.9049