Question
Asked Nov 8, 2019
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For a normal distribution, identify the z-score location that would separate the distribution into 2 sections so that there is

  1. 10% in the tail on the right-hand side
  2. 20% in the tail on the left-hand side
  3. 30% in the tail on the right-hand side
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Expert Answer

Step 1

1.

Step-by-step procedure to obtain the z-score location using MINITAB:

  • Choose Graph > Probability Distribution Plot choose View Probability > OK.
  • From Distribution, choose ‘Normal’ distribution.
  • Click the Shaded Area
  • Choose Probability and Right Tail for the region of the curve to shade.
  • Enter the Probability value as 10.
  • Click OK.

Output using the MINITAB software is given below:

Distribution Plot
Normal, Mean-0, StDev=1
0.4
0.3
0.2
0.1
0.1
0.0
1.282
X
Density
help_outline

Image Transcriptionclose

Distribution Plot Normal, Mean-0, StDev=1 0.4 0.3 0.2 0.1 0.1 0.0 1.282 X Density

fullscreen
Step 2

From the output, the z-score location that would separate the distribution into 2 sections so that there is 10% in the tail on the right-hand side is 1.282.

2.

Step-by-step procedure to obtain the z-score location using MINITAB:

  • Choose Graph > Probability Distribution Plot choose View Probability > OK.
  • From Distribution, choose ‘Normal’ distribution.
  • Click the Shaded Area
  • Choose Probability and Left Tail for the region of the curve to shade.
  • Enter the Probability value as 20.
  • Click OK.

Output using the MINITAB software is given below:

Distribution Plot
Normal, Mean-0, StDev=1
0.4
0.3
0.2
0.1
0.2
0.0
-0.8416
0
X
Density
help_outline

Image Transcriptionclose

Distribution Plot Normal, Mean-0, StDev=1 0.4 0.3 0.2 0.1 0.2 0.0 -0.8416 0 X Density

fullscreen
Step 3

From the output, the z-score location that would separate the distribution into 2 sections so that there is 20% in the tail on the Left-hand side is –0.8416.

3.

Step-by-step procedure to obtain the z-score location using MINITAB:

  • Choose Graph > Probability Distribution Plot choose View Probability > OK.
  • From Distribution, choose ‘Normal’ distribution.
  • Click the Shaded Area
  • Choose Probability...
Distribution Plot
Normal, Mean=0, StDev=1
0.4
0.3
0.2
0.1
0.3
0.0
0 0.5244
х
Density
O
help_outline

Image Transcriptionclose

Distribution Plot Normal, Mean=0, StDev=1 0.4 0.3 0.2 0.1 0.3 0.0 0 0.5244 х Density O

fullscreen

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