Normal Distributions
Excel’s NORM.INV Function
Learning Objectives
Use Excel’s NORM.INV() to calculate x-values related to given areas.
Left Area Given
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Right Area Given
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Middle Area Given
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Let us first look at an example where we calculate an -value when the left area is given.
Example 40.1.1
Problem Setup: Let us revisit the SAT score problem from the previous section. The average SAT score was 1,010 with a standard deviation of 20.
Question: What is the highest score for the bottom 85% of the students?
You try:
You try:
Conclusion: 85% of people score at most 1030.729 on their SATs.
Need Help? Go to the last section for a video that reviews all of the content in this section. You can also download a PowerPoint presentation on Normal Distributions.
Let us now look at an example where we calculate an -value when the right area is given.
Example 40.1.2
Problem Setup: Let us revisit the SAT score problem from the previous section. The average SAT score was 1,010 with a standard deviation of 20.
Question: Above what score do the top 15% of students score?
You try:
You try:
Conclusion: 15% of people score at least 1030.729 on their SATs.
Need Help? Click to reveal the solutions below OR go to the last section for a video explaining all content in this section.
When we are given the area to the right:
- We need to take a complement to get the area to the left
- This is because Excel’s NORM.INV() function works with areas to the left
- So, for the top 15%, this is the same as the bottom 85%:
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To calculate the -value associated with the above graphs, we use NORM.INV():
Let us finally look at an example where we calculate an -values when a middle area is given.
Example 40.1.3
Problem Setup: Let us revisit the SAT score problem from the previous section. The average SAT score was 1,010 with a standard deviation of 20.
Question: What is the range of SAT scores for the middle 85% of students?
You try:
You try:
You try:
You try:
You try:
Conclusion: 85% of students score between 981 and 1,038 on their SATs.
Need Help? Click to reveal the solutions below OR go to the last section for a video explaining all content in this section.
When we are given the middle area:
- We need to calculate the two -values separately
- Input the area to the left of and into NORM.INV
- The area to the left of :
- The area to the left of :
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To calculate the -value associated with the above graphs, we use NORM.INV:
Additional Resources:
- Click here to download the Powerpoint slides that accompany the video.
- Click here to download the Excel solutions for the Normal Distribution section.
Key Takeaways: Excel’s NORM.INV Function
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