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Find the height of a normal curve at a value

Use Normal PD to find the normal probability density at a given value, mean and standard deviation.

4 шага

Эта статья пока не переведена на русский. Показана полная английская версия.

Scores follow a normal distribution with mean and standard deviation . Find the height of the curve at , also called the normal probability density or normal pdf:

Find the density with Normal PD

Below each step is the screen you should see after pressing.

Next to each step is the screen you should see after pressing.

  1. Step 1

    Open the mode menu and tap Distribution.
    Press:
  2. Step 2

    Tap the type name at the top of the screen to open the Select Type sheet.
    Screen after step 2
  3. Step 3

    Tap Normal PD; its row may already be checked. The parameter boxes appear with selected.
    Screen after step 3
  4. Step 4

    Enter for and press the equals key, then enter for and press the equals key. Enter for . The result updates to ; you do not need to press the equals key after .
    Press:
    Screen after step 4

Read and check the height

The value row, labelled , shows . That is the height of the curve, so . On the curve picture, a dashed vertical line marks the height at .

This is a density, not a probability or a percentage. For a continuous normal variable, , and a density can exceed . To find the probability between two limits, use Normal CD instead: see find a normal probability.

To check the symmetry, tap the box, press AC once to empty it, then enter . It is the same distance from the mean as , so the screen shows the same height, .

If your result is different

  • You see a value before entering the example: a fresh screen shows for , and . A returning screen can keep earlier values. Enter all three example values before reading the answer.
  • The result becomes zero while you are typing: after entering for , the result is if and are still set. Finish entering and .
  • The box is dashed and the result shows Argument ERROR: the standard deviation must be positive. Tap the box, press AC once to empty it, then enter .
The fx-991EX Normal PD screen with x = 115, μ = 100, σ = 15 and p = 0.016 131 381 63.

Find a normal curve's height on your fx-991EX calculator

Enter x = 115, mean 100 and standard deviation 15 in Normal PD to find the curve's height at 115.