Question

find the area under the standard normal curve. use excel. round the answers to at least four decimal places.
part 1 of 4
(a) find the area under the standard normal curve that lies between z = -2.48 and z = -1.33.
the area between z = -2.48 and z = -1.33 is 0.0852.
part: 1 / 4
part 2 of 4
(b) find the area under the standard normal curve that lies outside the interval between z = -2.45 and z = -0.34.
the area outside the interval between z = -2.45 and z = -0.34 is

Explanation:

Step1: Recall the standard normal distribution property

The total area under the standard normal curve is \(1\). To find the area outside the interval \([-2.45, -0.34]\), we first find the area inside the interval and then subtract it from \(1\).

Step2: Find the area between \(z = -2.45\) and \(z=-0.34\)

Using the standard normal distribution (z - table or Excel function NORM.S.DIST), we calculate the area to the left of \(z=-0.34\) and the area to the left of \(z = - 2.45\), then subtract them.

• The area to the left of \(z=-0.34\) (using Excel: NORM.S.DIST(-0.34, TRUE)): Let's calculate it. The value is approximately \(0.3669\).
• The area to the left of \(z=-2.45\) (using Excel: NORM.S.DIST(-2.45, TRUE)): The value is approximately \(0.0071\).

The area between \(z=-2.45\) and \(z = - 0.34\) is \(0.3669-0.0071=0.3598\).

Step3: Find the area outside the interval

The total area under the curve is \(1\). So the area outside the interval \([-2.45,-0.34]\) is \(1 - 0.3598=0.6402\).

Answer:

\(0.6402\)