Question

Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1. 

The area of the shaded region is _______ (Round to four decimal places as needed.)

Answer 1

Solution:

Given:

We have to find area under curve for shaded region.

that is find:

P( -0.99 < Z < 1.27) =...............?

P( -0.99 < Z < 1.27) =P( Z < 1.27) - P( Z < -0.99 )

Look in z table for z = 1.2 and 0.07 as well as for  z = -0.9 and 0.09  and find corresponding area.

P( Z < 1.27) = 0.8980

and

P( Z< -0.99) = 0.1611

Thus

P( -0.99 < Z < 1.27) =P( Z < 1.27) - P( Z < -0.99 )

P( -0.99 < Z < 1.27) =0.8980 - 0.1611

P( -0.99 < Z < 1.27) =0.7369

The area of the shaded region is: 0.7369