Question

Find the area under the standard normal curve to the right of the following z-values. Round your answer to four decimal places.

(a) Find the area under the standard normal curve to the right of =z0.51.

(b) Find the area under the standard normal curve to the right of =z1.82.

(c) Find the area under the standard normal curve to the right of =z2.46.

(d) Find the area under the standard normal curve to the right of =z−2.35.

Answer 1

Solution:

We have to find the area under the standard normal curve to the right of the following z-values.

Part a) z = 0.51

Find:

P( Z > 0.51 ) = ..............?

P( Z > 0.51 ) = 1 - P( Z < 0.51 )

Look in z table for z = 0.5 and 0.01 and find corresponding area.

P( Z < 0.51) = 0.6950

thus

P( Z > 0.51 ) = 1 - P( Z < 0.51 )

P( Z > 0.51 ) = 1 - 0.6950

Part b) z = 1.82

Find:

P( Z > 1.82) = ..............?

P( Z > 1.82) = 1 - P( Z < 1.82)

Look in z table for z = 1.8 and 0.02 and find corresponding area.

P( Z < 1.82) = 0.9656

Thus

P( Z > 1.82) = 1 - P( Z < 1.82)

P( Z > 1.82) = 1 -0.9656

Part c) z = 2.46

Find:

P( Z > 2.46) = ..............?

P( Z > 2.46) = 1 - P( Z < 2.46)

Look in z table for z = 2.4 and 0.06 and find corresponding area.

P( Z < 2.46) = 0.9931

thus

P( Z > 2.46) = 1 - P( Z < 2.46)

P( Z > 2.46) = 1 - 0.9931

Part d) z = -2.35

Find:

P( Z > -2.35) = ..............?

P( Z > -2.35) = 1 - P( Z < -2.35)

Look in z table for z = -2.3 and 0.05 and find corresponding area.

P( Z < -2.35) = 0.0094

thus

P( Z > -2.35) = 1 - P( Z < -2.35)

P( Z > -2.35) = 1 -0.0094