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# CALC 1 Binomial Distribution Calculator

This calculator performs calculations involving the Binomial Distribution including the CDF, inverse and plotting. ## Calculator Keys Examples

### cdf key, the cumulative distribution function.

Value Keystrokes Display Description
.6 prob 0.600 Enters the probability value.
5 trials 5.00 Enters the number of trials value.
3 sccs 3.00 Enters the number of successes value.

cdf 0.663 Calculates the cdf.

### cdf key, the probability mass function.

Value Keystrokes Display Description
.6 prob 0.600 Enters the probability value.
5 trials 5.00 Enters the number of trials value.
3 sccs 3.00 Enters the number of successes value.

pmf 0.346 Calculates the pdf.

### sccs key, the inverse cumulative distribution function.

Value Keystrokes Display Description
.6 prob 0.600 Enters the probability value.
5 trials 5.00 Enters the number of trials value.
.9 cdf 0.900 Enters the cdf value.

sccs 4.00 Calculates the inverse cdf.

### trials key, the number of trials for pmf, 0 sccs and prob.

In some cases you wish to calculate the number of trials for a given prob and pmf.

Value Keystrokes Display Description
.01 prob 0.01 Enters the probability value.
.5 pmf 0.500 Enters the pmf value.

trials 69 Calculates the number of trials.

pmf 0.4998 Calculates the actual pmf for the number of trials.

Note that the sccs value is set to 0 for this calculation.

### 1-x key

This key is a quick calculation of p values to convert form lower to upper tail.

Value Keystrokes Display Description
0.95 1 - x .05 Calculates 1 - x.

### plot(x,y) using the shift +/- 3s key.

This key will create a plot for the number of sccs between x and y.
We will use the shift +/- 3s key to calculate the x and y values for the given trials and prob.

Value Keystrokes Display Description
0.7 prob 0.70 Enters the prob value..
100 trials 100 Enters the trials value..

shift+/-3s 57.0 Calculates the upper (reg y) and lower values for the plot.

plot(x,y)
Generates the plot. Any valid values for sccs can be used for the upper and lower limits of the plot.
The minimum and maximum values can be in any order.

### mean key

This key calculates the mean of the distribution.

Value Keystrokes Display Description
0.7 prob 0.70 Enters the prob value.
100 trials 100 Enters the trials value.

mean 70.0 Calculates the mean of the distribution.

### sd key

This key calculates the standard deviation of the distribution.

Value Keystrokes Display Description
0.7 prob 0.70 Enters the prob value.
100 trials 100 Enters the trials value.

sd 4.58 Calculates the standard deviation of the distribution.

## Shifted Keys

### +/- 3s key.

This key will calculate 2 values for sccs that will contain +/- 3 standard deviations, or about 0.997 of outcomes
This is useful for calculating values for plots.

Value Keystrokes Display Description
0.7 prob 0.70 Enters the prob value..
100 trials 100 Enters the trials value..

shift+/-3s 57.0 Calculates the upper (reg y) and lower values for the plot.

SWAP 84.0
Displays the upper value.

### rand(x,y) key, returns a random number between x and y.

Value Keystrokes Display Description
52 = or ENTER 52.0 Enters the y value
1 rand(x,y) A random number from 1 - 52. Enters the x value, then returns a random number between x and y.

To repeat, press the ROLL key to roll the x and y values down, then press rand(x,y).
The minimum and maximum values can be in any order.

### odds(p) key, the odds (failures to y and successes to x) for the given p.

Value Keystrokes Display Description
.55 odds(p) 11
(successes)
Calculates the odds (failures to y and successes to x) for the given p.
SWAP 9
(failures)
Displays the failures.

### p(f,s) key, the p for the entered failures and success.

Value Keystrokes Display Description
11 = or ENTER 11 Enters the failures value
13 p(f,s) 0.542 Enters the successes value, then calculates the p for the entered failures and success.

## Common Keys

The reference for keys not covered here can be found in the Basic SR Calculator documentation.
Long press any key to display a description for that key.