Distributions

To enter the Distributions application, highlight the app using the directional keys. Press the ok key to enter the application. This app allows you to study different probability distributions such as Binomial, Normal, Chi-squared and many others.

Getting started

Calculate a probability

The Distributions application allows you to calculate probabilities from a continuous or discrete probability distribution. It is structured in 3 steps:

Step 1: Choose the probability distribution

Highlight the probability distribution you would like to use with the directional arrows. Then confirm by pressing ok to continue to the next step.

You may choose between 6 continuous distributions and 3 discrete distributions.

Continuous distributions:

• Uniform distribution
• Exponential distribution
• Normal distribution
• Chi-square distribution
• Student’s t-distribution
• Fisher’s F-distribution

Discrete distributions:

• Binomial distribution
• Geometric distribution
• Hypergeometric distribution
• Poisson distribution

Step 2: Enter the parameters

Now that you have selected a distribution, you must enter your desired parameters. To do this:

1. Enter the value of the parameter(s)
2. Highlight Next.
3. Confirm with the ok key. This will take you to the next step.

The following list includes the parameters for each distribution:

• Binomial
  • $n$ : number of trials
  • $p$ : success probability
• Uniform
  • $a$, $b$ : bounds of the interval
• Exponential
  • $\lambda$ : parameter
• Normal
  • $\mu$ : mean
  • $\sigma$ : standard deviation
• Chi-square
  • $k$ : degrees of freedom
• Student’s t
  • $k$ : degrees of freedom
• Geometric
  • $p$ : success probability
• Hypergeometric
  • $N$ : population size
  • $K$ : total of items with feature
  • $n$ : sample size
• Poisson
  • $\lambda$ :parameter
• Fisher’s F
  • $d1$ : degrees of freedom of the numerator
  • $d2$ : degrees of freedom of the denominator

Step 3: Calculate probabilities

Calculating a probability

To calculate a probability:

1. Highlight the bound in which you need to enter your value.
2. Enter the value.
3. Confirm by pressing the ok key.

You may now read the result of the probability calculation.

Modifying the bounds

You can modify the type of bounds for your probability calculations.

• $$X≤a$$
• $$a≤X$$
• $$a≤X≤b$$
• $$X=a$$

The last option may only be used for discrete distributions.

To modify the bounds of your probability calculation:

1. Navigate to the image at the top left of the screen.
2. Confirm with the ok key.
3. A drop-down menu opens. Choose the type of bounds you would like.
4. Confirm with the ok key.

You have changed the type of bounds for calculating your probabilities.

Calculating the inverse

You may calculate $a$ in $P(a≤X)=p$ for a given $p$ probability value. To do so:

1. Highlight the field in which the probability value is located.
2. Enter your value.
3. Confirm by pressing the ok key.

The calculator will display the value of $a$.

Solving for μ and σ

You may calculate the value of μ or σ from a Normal probability distribution.

To do this, simply leave the value to be calculated (μ or σ) blank in the second step and then enter the value of the probability. The calculator will then give the requested value below the graph.