How to Use invNorm on the TI-84 Evo

On the TI-84 Evo, invNorm is in the DISTR menu: press alpha, then stat, and pick it under Normal. It works backwards from normalcdf: you give it an area (a share of the scores), the mean and the standard deviation, and it gives you the score that cuts off that share.

The example here: test scores with a mean of 75 and a standard deviation of 10. What score sits at the 90th percentile?

Find the score at a percentile

  1. Press alpha, then stat. DISTR is the green label above the stat key, so this opens the distribution menu.
    The TI-84 Evo DISTR menu with 1: Normal highlighted at the top
  2. Press enter to open Normal.
  3. Press the down arrow to invNorm(, then press enter. That opens the InvNorm setup screen.
    The Normal menu on the TI-84 Evo with 3: invNorm( highlighted, below normalpdf( and normalcdf(
  4. Type the three numbers, pressing the down arrow after each one. Typing replaces whatever is already in a box.
    • area is the share of scores on one side of the score you want, as a decimal. The 90th percentile has 90% of scores below it: .9.
    • μ is the mean: 75.
    • σ is the standard deviation: 10.
  5. Press enter on the tail row to select LEFT. The tail row says which side of the score the area is on, and LEFT means below it. The last down arrow already put the cursor on LEFT. The selected tail is the one filled in dark.
    The InvNorm setup screen on the TI-84 Evo with area .9, mu 75, sigma 10 and tail LEFT selected, and a PASTE button at the bottom
  6. Press zoom. The zoom key works the PASTE button at the bottom of the screen, which puts the finished command on the home screen.
  7. Press enter. The answer is 87.81551567, so a score of about 87.8 is the 90th percentile.
    The TI-84 Evo home screen showing invNorm(.9,75,10,LEFT) equals 87.81551567

The top percent of scores: RIGHT

What score gets you into the top 5%? That 5% sits above the score, on the right side, so this one uses the RIGHT tail.

  1. Press alpha, stat, enter, then the down arrow to invNorm( and enter. The setup screen still holds 75 and 10 from last time.
  2. Type .05 in area.
  3. Press the down arrow to the tail row, then the right arrow to RIGHT. The cursor always starts the tail row on LEFT.
  4. Press enter to select RIGHT. RIGHT is now selected. Moving the cursor onto a tail doesn't select it; only enter does.
    The InvNorm setup screen with area .05, mu 75, sigma 10 and tail RIGHT selected
  5. Press zoom, then enter. The answer is 91.44853626, so it takes about 91.4 to land in the top 5%.
    The TI-84 Evo home screen with invNorm(.05,75,10,RIGHT) equals 91.44853626 below the 90th percentile result

The middle percent of scores: CENTER

CENTER puts the area in the middle and gives both ends of that range at once. For the middle 95% of scores:

  1. Open invNorm again and type .95 in area.
  2. Press the down arrow to the tail row, the right arrow once to CENTER, then enter.
  3. Press zoom, then enter. The answer comes back in braces with two numbers, the low end first: the middle 95% of scores fall between about 55.4 and 94.6.
    The TI-84 Evo home screen with invNorm(.95,75,10,CENTER) equals the list 55.40036014, 94.59963986 below the two earlier results

Good to know

  • Getting ERROR: DOMAIN? The area has to be a decimal between 0 and 1. Typing 90 for 90% gives this error. Choose Quit, reopen invNorm and type .9.
  • The setup screen remembers your last numbers and tail. Check all four boxes before you paste.
  • Prefer to stick with LEFT? For the top 5%, type the area below the score instead: invNorm(.95, 75, 10, LEFT) gives the same 91.44853626.
  • For z-scores, set μ to 0 and σ to 1. The z-score at the 95th percentile is invNorm(.95, 0, 1, LEFT) = 1.644853626.
  • Following a video made on another TI-84? Those open the distribution menu with 2nd, vars. On the Evo that opens the MATRIX menu, and DISTR is alpha, stat.
  • Have a score and need the probability? That's normalcdf, right above invNorm in the Normal menu.