Find a probability on a normal curve

Work out the chance that a normally distributed value lands between two numbers.

Many measurements, such as heights or test scores, follow a bell-shaped curve defined by a mean (μ) and a standard deviation (σ). The probability of landing between two numbers is the area under the curve between them.

The example: scores have a mean of 100 and a standard deviation of 15. What is the chance a score is between 90 and 110? The answer is about 0.4950, or 49.5 percent.

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 with 2nd then vars, and choose normalcdf(.
2ndDISTRvars2
Fill in the form: lower 90, upper 110, μ 100, σ 15. Press down after each number.
90▼110▼100▼15▼
Select Paste to send the command to the home screen, then press enter to calculate.
enterenter

You should seenormalcdf(90,110,100,15) .4950149249

Classic Graphing 84 key reference

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 Normal CD.
MENU72
Answer the prompts in order: lower 90, upper 110, σ 15, then μ 100. Press = after each.
90=110=15=100=

You should seeNormal CD p=0.4950149249

Watch the order: this model asks for σ before μ.

Natural Scientific 991 key reference

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).
MENU2F5F1
Choose Ncd (F2) and fill in the form: lower 90, upper 110, σ 15, μ 100. Press EXE after each, and once more to run it.
F290EXE110EXE15EXE100EXEEXE

You should seeNormal C.D p=0.4950149249

Natural Color Graphing key reference

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.

Open the Probability menu and choose normCdf(.
menu56
Type lower, upper, μ and σ separated by commas, close the bracket and press enter.
90,110,100,15)enter

You should seenormCdf(90,110,100,15) 0.495015

Classic CAS key reference

Tips

To get a one-sided probability, use a very large number as the other end, for example 1E99 for "above" or -1E99 for "below".
If you leave μ and σ out, most models assume the standard curve with μ = 0 and σ = 1.