# Answer to Question #8379 in Statistics and Probability for dustin hanshaw

Question #8379

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

Expert's answer

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

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

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