Distribution App

The Distribution app can handle binomial distribution, normal distribution, Poisson distribution, and a variety of other types of probability distribution.

1. h > Distribution

This displays the distribution selection menu.



2. Highlight the distribution you want to use for calculation and then press > (or O).

You can choose from among the distributions below.

Discrete distribution

Binomial distribution

Poisson distribution

Geometric distribution

Hypergeometric distribution

Continuous Distribution

Normal distribution

Student-t distribution

${\chi }^2$ distribution

F distribution

1. Select a tail setting for probability calculation.

1. Highlight [Tail] and then press O.

2. From the menu that appears, select one of the options described below.



[]:

Calculates the cumulative probability for specified data value $x$ or lower.

[]:

Calculates the cumulative probability for the lower (Lower) and upper (Upper) boundaries of the data values.

[]:

Calculates the cumulative probability for specified data value $x$ or higher.

[]:

Calculates the probability for given data value $x$ (discrete distribution only).

2. Specify whether to use a single data value or multiple data values for the calculation.

1. Highlight [Data] and then press O.

2. Select [Variable] to use a single data value for calculation or [List] for multiple data values.

3. Input the other parameters.

Parameters common to all distributions

Input the parameters below according to what you specified for [Tail] (step 3) and [Data] (step 4).

Tail Data	, ,
Variable	$x$: Data value	Lower: Data value lower limit Upper: Data value upper limit
List	List*1: List to use as data values	L.List*1: List to use as the lower boundary of data values U.List*1: List to use as the upper boundary of data values

For the operation to specify a list variable to use as data values, see To specify a list variable to use as data values.

Distribution Type Specific Parameters

Binomial distribution

Numtrial: Number of trials

p: Probability of success (0 ≤ p ≤ 1)

Normal distribution

DisplayZ: Displays Z-Scores^*2

μ: Population mean

σ: Population standard deviation (σ > 0)

Poisson distribution

λ: Mean (λ > 0)

Geometric distribution

p: Probability of success (0 < p ≤ 1)

Hypergeometric distribution

n: Number of trials from population (0 ≤ n integer)

M: Number of successes in population (0 ≤ M integer)

N: Population size (n ≤ N, M ≤ N integer)

Student-t distribution

df: Degrees of freedom (df > 0)

${\chi }^2$ distribution

df: Degrees of freedom (Positive integer)

F distribution

n:df: Degrees of freedom of numerator (Positive integer)

d:df: Degrees of freedom of denominator (Positive integer)

Select [On] to show Z-scores (standardized values) or [Off] to hide them. If you choose [On], calculation is performed as μ = 0 and σ = 1.

Note

You can specify the color of the graph by highlighting [Color] and then pressing O (only if you chose [Data] > [Variable] in step 4).

Selecting T > [Input Descriptions] displays explanations of the parameters.

1. On the Setup tab, press >, or highlight and then press O.

Calculation results are displayed on the Results tab.



Single Data Value Calculation

(When [Data] > [Variable] selected.)



Multiple Data Value Calculation

(When [Data] > [List] selected.)

When [Data] > [List] is selected on the Setup tab, use the following operation to specify the list variable to use as data values. The operations in steps 2 through 5 below are not necessary if you use a list variable that has already been saved.

1. On the Setup tab, highlight [List], [L.List], or [U.List] and then press O.

2. On the menu that appears, highlight [List Editor] and then press O.

This displays List Editor.

3. Input data values in any one of the lists (List 1 through List 26).

For information about the input operation, see Inputting Data in List Editor.

4. After you finish inputting the data, press b.

5. Press O.

6. On the menu that appears, highlight [Select List] and then press O.

7. Use the dialog that appears to input a list number and then press O.

Highlight the value of $x$, Lower, or Upper and then use the number keys or select T > [Edit/View Value] to change the value.

P (X ≤ $x$ ) = p

P ( Lower ≤ X ≤ Upper ) = p

P (X ≥ $x$ ) = p

P (X = $x$ ) = p^*

Discrete distribution only

Highlight the $p$-value and then use the number keys or select T > [Edit/View Value] to change the value.

P (X ≤ $x$) = p

P (Lower ≤ X ≤ Upper) = p^*

P (X ≥ $x$) = p

Normal distribution only

From the menu that appears when you select T > [Tail], select the option you want. For information about available options, see step 3 under Operation Flow.

Note that in the below conditions, calculations are performed as ${\infty =9.99\times 10}^{99}$, ${\mathrm{-\infty }=-9.99\times 10}^{99}$.

The result of an inverse calculation of a discrete distribution is an integer. Precision is reduced if the cumulative probability $p$ you input has 10 or more digits.

The following conditions cause an error (Out of Domain).