Question

Sketch the areas under the standard normal curve over

theindicated intervals, and find the specified areas.
a)To the left of z = 0.72.
b)To the right of z = 0.15.
c)Between z = -1.40 and z = 2.03.

Answer 1

a)
`P(Z<0.72)=0.764`

b)
`P(Z>0.15)=1-0.560=0.440`

c)
`P(-1.40<Z<2.03)=0.979-0.081=0.898`

Explanation:

a)To the left of z = 0.72.

For this case the shaded area is on the figure 1 attached.

And we can find the area with the normal standard table of with the following excel code:

=NORM.DIST(0.72,0,1,TRUE)

`P(Z<0.72)=0.764`

b)To the right of z = 0.15.

For this case the shaded area is on the figure 2 attached.

And we can find the area with the normal standard table of with the following excel code:

=1-NORM.DIST(0.15,0,1,TRUE)

`P(Z>0.15)=1-0.560=0.440`

c)Between z = -1.40 and z = 2.03.

For this case the shaded area is on the figure 3 attached.

And we can find the area with the normal standard table of with the following excel code:

=NORM.DIST(2.03,0,1,TRUE)-NORM.DIST(-1.40,0,1,TRUE)

`P(-1.40<Z<2.03)=0.979-0.081=0.898`