Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard
deviation 1.
-
A) 0.4656
B) -0.0344
C) 0.9656
D) 0.0344

Question

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard
deviation 1.
-
A) 0.4656 
B) -0.0344 
C) 0.9656 
D) 0.0344

Quizplus · Accepted Answer

To find the area of the shaded region, we need to find the area to the left of z=2.30 and the area to the right of z=-0.80, and then subtract the two areas. Using a standard normal distribution table or calculator, we can find:

- area to the left of z=2.30 is 0.9893
- area to the right of z=-0.80 is 0.7881

Subtracting the two areas, we get:

0.9893 - 0.7881 = 0.2012

So the area of the shaded region is 0.2012. However, notice that the shaded region is to the right of the mean (z=0), so this area represents the probability of observing a value greater than the mean. To get the probability of observing a value less than the mean (which is the standard definition of area under the curve), we need to subtract the shaded area from 1:

1 - 0.2012 = 0.7988

Therefore, the area under the curve to the left of z=2.30 and to the right of z=-0.80 (which includes the shaded region) is 0.7988.

Find the Area of the Shaded Region