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 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 0.6402.
part 3 of 4
(c) find the area under the standard normal curve to the left of z = -2.16.
the area to the left of z = -2.16 is 0.0154.
part 4 of 4
(d) find the area under the standard normal curve to the right of z = -0.4.
the area to the right of z = -0.4 is

Explanation:

Step1: Recall the standard normal distribution property

The total area under the standard normal curve is 1. To find the area to the right of \( z = -0.4 \), we can use the property that the area to the right of a z - score \( z \) is \( 1 - P(Z\leq z) \), where \( P(Z\leq z) \) is the cumulative probability up to \( z \).

Step2: Use Excel or z - table to find \( P(Z\leq - 0.4) \)

Using the standard normal distribution (z - table or Excel function NORM.S.DIST(-0.4, TRUE)), we find that \( P(Z\leq - 0.4)\approx0.3446 \).

Step3: Calculate the area to the right

The area to the right of \( z=-0.4 \) is \( 1 - 0.3446 = 0.6554 \).

Answer:

\( 0.6554 \)