Natural Scientific 991 manual · Chapter 13 of 18

Probability distributions

Normal, binomial and Poisson probabilities, plus the inverse normal.

13.1Open the Distribution app#

Press MENU then 7.

Number	Item	Asks for
1	Normal PD	x, σ, μ
2	Normal CD	Lower, Upper, σ, μ
3	Inverse Normal	Area, σ, μ
4	Binomial PD	x, N, p
5	Binomial CD	x, N, p
6	Poisson PD	x, λ
7	Poisson CD	x, λ

Fill in the form pressing = after each box. For σ and μ the standard values 1 and 0 are already filled in; just press = to accept them. After the last box the answer appears. Press = or AC to go back and try again.

The Distribution menu The display shows: 1:Normal PD / 2:Normal CD / 3:Inverse Normal / 4:Binomial PD. — The Distribution menu

13.2Normal distribution probabilities#

Normal PD gives the height of the bell curve at x. Normal CD gives the probability that a value falls between a lower and upper limit. Inverse Normal gives the value x with a given area to its left.

Example 13.1

Normal PD at 0

Normal PD, x = 0, keep σ = 1 and μ = 0.
MENU710=1=0=

Example 13.2

Within one standard deviation

P(-1\le Z\le 1)

Normal CD from -1 to 1, with σ = 1 and μ = 0.
MENU72(−)1=1=1=0=

Result of the example "Within one standard deviation" The display shows: Normal CD / p=0.6826894921. — You should see`p=0.6826894921`

Example 13.3

With your own mean and spread

Between 90 and 110, σ = 10, μ = 100.
MENU7290=110=10=100=

Example 13.4

Inverse normal

Area 0.975 with σ = 1, μ = 0.
MENU730.975=1=0=

f(x)=\frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}

The normal density that Normal PD evaluates

13.3Binomial probabilities#

Binomial PD is the probability of exactly x successes in N tries when each try has probability p. Binomial CD is the probability of x or fewer. N and x must be whole numbers and p must be between 0 and 1.

Example 13.5

Exactly 3 heads in 5 flips

Binomial PD: x = 3, N = 5, p = 0.5.
MENU743=5=0.5=

Example 13.6

At most 2 heads in 4 flips

Binomial CD: x = 2, N = 4, p = 0.5.
MENU752=4=0.5=

P(X=x)=\binom{N}{x}p^x(1-p)^{N-x}

Binomial probability

13.4Poisson probabilities#

Poisson PD is the probability of exactly x events when the average is λ. Poisson CD is the probability of x or fewer.

Example 13.7

Poisson PD

x = 2, λ = 3.
MENU762=3=

Example 13.8

Poisson CD

x = 2, λ = 3.
MENU772=3=

P(X=x)=\frac{\lambda^x e^{-\lambda}}{x!}

Poisson probability

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