If X ~ N(2, 9), compute

a. P(X ≥ 2)

b. P(l ≤ X ≤ 7)

c. P(‒2.5 ≤ X ≤ ‒1)

d. P(‒3 ≤ X ‒ 2 ≤ 3)

Step 1 of 4:

Here .

Here mean and

Variance

Then, standard deviation

Therefore standard deviation .

Our goal is:

a). We need to find .

b). We need to find .

c). We need to find .

d). We need to find .

a).

Now we have to compute the .

The formula of the z is

z=

We know that mean 2 and standard deviation 3.

Then,

= 1-

Using area under the normal curve table.

=0.5000.

= 1- 0.5000

= 0.5000

Therefore is 0.5000.

Step 2 of 4:

b).

Now we have to find .

The formula of the z is

z=

We know that2 and 3.

=

=

=and

=

=

=

Using area under the normal curve table.

Therefore is 0.5808.