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Natural Color Graphing manual · Chapter 14 of 18

Probability distributions

Normal, t, chi-squared, F, binomial, Poisson and geometric distributions.

14.1Open the distribution menu#

In Statistics press F5 (DIST). The bar lists NORM, T, CHI, F, BINOMIAL, POISN and GEO (some on a second page). Choose one, then P.D (the height or probability of one value), C.D (the cumulative probability) or Inverse (the value for a probability). Fill in the form, pressing EXE after each field; defaults are already filled in.

F keyGroupItems
F1NORMNpd, Ncd, InvN
F2Ttpd, tcd, Invt
F3CHICpd, Ccd, InvC
F4FFpd, Fcd, InvF
F5BINOMIALBpd, Bcd, InvB
F6 then F1POISNPpd, Pcd, InvP
F6 then F2GEOGpd, Gcd, InvG
The DIST bar The display shows: List 1 | List 2 | List 3 | List 4 | List 5 | List 6 / | | | | | / List 1[1]= / NORM T CHI F BINOMIAL ▷.
The DIST bar

14.2Normal distribution#

f(x)=1σ2πe−(x−μ)22σ2f(x)=\frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}
The normal density (Npd)
Example 14.1

Normal C.D from -1 to 1

  1. DIST, NORM, Ncd, then calculate.

    MENU2F5F1F2F1
Result of the example "Normal C.D from -1 to 1" The display shows: Normal C.D / p=0.6826894921 / z:Low=-1 / z:Up=1.
You should seeNormal C.D p=0.6826894921
Example 14.2

Normal P.D at 0

  1. DIST, NORM, Npd, calculate.

    MENU2F5F1F1F1
Result of the example "Normal P.D at 0" The display shows: Normal P.D / p=0.3989422804.
You should seep=0.3989422804
Example 14.3

Inverse normal

  1. Left tail, area 0.95.

    MENU2F5F1F3▼F1
Result of the example "Inverse normal" The display shows: Inverse Normal / xInv=1.644853627.
You should seexInv=1.644853627
Example 14.4

Central inverse normal

  1. Central tail, area 0.95.

    MENU2F5F1F3F3▼F1
Result of the example "Central inverse normal" The display shows: Inverse Normal / x1InvN=-1.959963985 / x2InvN=1.959963985.
You should seex1InvN=-1.959963985 x2InvN=1.959963985

14.3t, chi-squared and F#

Example 14.5

Student t C.D

  1. DIST, T, tcd, calculate.

    MENU2F5F2F2F1
Result of the example "Student t C.D" The display shows: Student-t C.D / p=0.5 / t:Low=-1 / t:Up=1.
You should seep=0.5
Example 14.6

Inverse chi-squared

  1. DIST, CHI, InvC, calculate.

    MENU2F5F3F3F1
Result of the example "Inverse chi-squared" The display shows: Inverse χ² / xInv=3.841458821.
You should seexInv=3.841458821
Example 14.7

Inverse F

  1. DIST, F, InvF, calculate.

    MENU2F5F4F3F1
Result of the example "Inverse F" The display shows: Inverse F / xInv=161.4476388.
You should seexInv=161.4476388

14.4Binomial, Poisson and geometric#

P(X=x)=(Nx)px(1−p)N−xP(X=x)=\binom{N}{x}p^x(1-p)^{N-x}
Binomial probability
P(X=x)=μxe−μx!P(X=x)=\frac{\mu^x e^{-\mu}}{x!}
Poisson probability
Example 14.8

Binomial P.D

  1. x = 2, Numtrial = 5, p = 0.5.

    MENU2F5F5F12EXE5EXEEXEEXE
Result of the example "Binomial P.D" The display shows: Binomial P.D / p=0.3125.
You should seep=0.3125
Example 14.9

Poisson P.D

  1. x = 2, μ = 3.

    MENU2F5F6F1F12EXE3EXEEXE
Result of the example "Poisson P.D" The display shows: Poisson P.D / p=0.2240418077.
You should seep=0.2240418077
Example 14.10

Geometric C.D

  1. x = 3, p = 0.5.

    MENU2F5F6F2F23EXEEXEEXE
Result of the example "Geometric C.D" The display shows: Geometric C.D / p=0.875.
You should seep=0.875

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