Question

The values of z-score are given.

A) Find the area under the normal curve to the right of z = -0.84. Round the answer to four decimal places.

B)   Find the area under the normal curve between z = 0.43 and z = 1.33. Round the answer to four decimal places.

C)   Find the area under the normal curve between z = -0.32 and z = 0.92. Round the answer to four decimal places.

D)   Find the area under the normal curve outside z = -1.52 to z = -0.47. Round the answer to four decimal places.

Please help me understand how to do this problem not just numbers, thank you!

Answer 1

The area under the normal curves are calculated by findidng the area for the respective z-scores from the z-tables

The z-tables attached below give us the area to the left of the z-scores

Question (a)

The area under the normal curve to the right of z = -0.84

The area under normal curve to the left of z-score -0.84 can be found from the negative z-table attached below

The area under normal curve to the left of z-score -0.84 is 0.20045

We know that area under normal curve = 1

Area to the left of z-score + Area to the right of z-score = 1

0.20045 + Area to the right of z-score = 1

Area to the right of z-score = 1 - 0.20045

= 0.79955

= 0.7996 rounded to 4 decimal places

The area under the normal curve to the right of z score -0.84 = 0.7996

Question (b)

The area under the normal curve between z = 0.43 and z = 1.33

we will first find the area to the left of z = 0.43 and then subtract if from the area to the left of z = 1.33 to get the area under the normal curve between z = 0.43 and z = 1.33

The area under normal curve to the left of z-score 0.43 can be found from the positive z-table attached below

The area under normal curve to the left of z-score 0.43 is 0.66640

The area under normal curve to the left of z-score 1.33 can be found from the positive z-table attached below

The area under normal curve to the left of z-score 1.33 is 0.90824

The area under the normal curve between z -score 0.43 and z -score 1.33 = 0.98024 - 0.66640

= 0.31384

= 0.3138 rounded to 4 decimal places

Question (c)

The area under the normal curve between z = -0.32 and z = 0.92

we will first find the area to the left of z = -0.32 and then subtract if from the area to the left of z = 0.92 to get the area under the normal curve between z = -0.32 and z = 0.92

The area under normal curve to the left of z-score -0.32 can be found from the negative z-table attached below

The area under normal curve to the left of z-score -0.32 is 0.37448

The area under normal curve to the left of z-score 0.92 can be found from the positive z-table attached below

The area under normal curve to the left of z-score 0.92 is 0.82121

The area under the normal curve between z -score -0.32 and z -score 0.92 = 0.82121 - 0.37448

= 0.44673

= 0.4467 rounded to 4 decimal places

Question (d)

The area under the normal curve between z = -1.52 to z = -0.47

we will first find the area to the left of z = -1.52 and then subtract if from the area to the left of z = -0.47 to get the area under the normal curve between z = -1.52 and z = -0.47

The area under normal curve to the left of z-score -1.52 can be found from the negative z-table attached below

The area under normal curve to the left of z-score -1.52 is 0.06426

The area under normal curve to the left of z-score -0.47 can be found from the positive z-table attached below

The area under normal curve to the left of z-score -0.47 is 0.31918

The area under the normal curve between z -score -1.52 and z -score -0.47 = 0.31918 - 0.06426

= 0.25492

= 0.2549  rounded to 4 decimal places