Find the value for a given percentile
Go backwards from an area on the normal curve to the number that cuts it off.
Inverse normal answers the question: below which value does a given share of the data lie? On the standard curve, the 97.5th percentile is 1.96, the familiar value for 95 percent confidence.
The example uses scores with mean 100 and standard deviation 15. The 97.5th percentile is about 129.40.
Classic Graphing 84
Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.
Open the DISTR menu (2nd then vars) and choose invNorm(.
2ndDISTRvars3Fill in area 0.975, μ 100, σ 15. Press down after each number and keep the tail set to LEFT.
0.975▼100▼15▼▼Select Paste, then press enter to calculate.
enterenter
You should seeinvNorm(0.975,100,15) 129.3994598
Classic Graphing 84 key reference · Classic Graphing 84 manual
Natural Scientific 991
Start on the main screen: Press MENU, then 1 (Calculate) to return to the main calculation screen. AC clears the line you are on.
Open the Distribution mode and choose Inverse Normal.
MENU73Answer the prompts: area 0.975, then σ 15, then μ 100. Press = after each.
0.975=15=100=
You should seeInverse Normal xInv=129.3994598
Natural Scientific 991 key reference · Natural Scientific 991 manual
Natural Color Graphing
Start on the main screen: Press MENU then 1 to open Run-Matrix, the main calculation screen. Press EXIT to back out of a bar or screen, and SHIFT then EXIT (QUIT) to return to the app start.
Open the Stat mode, then DIST (F5), then NORM (F1), and choose InvN (F3).
MENU2F5F1F3Move down to the Area box and fill in area 0.975, σ 15, μ 100, pressing EXE after each. Press EXE once more to run it.
▼0.975EXE15EXE100EXEEXE
You should seeInverse Normal xInv=129.3994598
Natural Color Graphing key reference · Natural Color Graphing manual
Classic CAS
Start on the main screen: Press home to open the Home menu (Calculator, Graphs, Settings, and more). Choose Calculator, or press esc to go back to the calculation page.
Type invNorm( by hand (it is also in the Probability menu). Give it the area, then μ and σ.
invnorm(0.975,100,15)Press enter.
enter
You should seeinvnorm(0.975,100,15) 129.399
Tips
- The area is always the share to the LEFT of the answer unless you change the tail setting.