# Binomial Distribution Calculator Binomial Probability Calculator, Binomial CDF calculations Using the blue padlock icons next to the Throw Distance value or Image Size value you can have
the Zoom Range slider only affect one of the two controls. If you press the blue padlock icon next to the Throw Distance value so that the
icon shows a Lock symbol, then moving the Zoom Slider will only adjust the Image Size bigger or smaller as would be visually represented if
you turned the Zoom Lens ring on your projector’s zoom lens to make the image bigger or smaller. If you click the padlock next to the Image Size
value so that the icon shows a Lock symbol, then moving the Zoom Slider will only adjust the Throw Distance position of the projector
in your room. The position of the projector in your room changes because you will need to move the projector closer or further away from the screen
to maintain the same image size to match your screen when turning the zoom lens ring. Therefore, the cumulative binomial probability is simply the sum of the probabilities for all events from 0 to x. Our binomial distribution calculator uses the formula above to calculate the cumulative probability of events less than or equal to x, less than x, greater than or equal to x and greater than x for you. A projection calculator is used to calculate a screen size when a projector is a specific distance away from the screen.

## Calculate probabilities of the binomial distribution step by step

Use this binomial probability calculator to easily calculate binomial cumulative distribution function and probability mass given the probability on a single trial, the number of trials and events. It can calculate the probability of success if the outcome is a binomial random variable, for example if flipping a coin. Under the same conditions you can use the binomial probability distribution calculator above to compute the number of attempts you would need to see x or more outcomes of interest (successes, events). For example, if you know you have a 1% chance (1 in 100) to get a prize on each draw of a lottery, you can compute how many draws you need to participate in to be 99.99% certain you win at least 1 prize (917 draws). Note that this example doesn’t apply if you are buying tickets for a single lottery draw (the events are not independent).

• Use this binomial probability calculator to easily calculate binomial cumulative distribution function and probability mass given the probability on a single trial, the number of trials and events.
• We are not to be held responsible for any resulting damages from proper or improper use of the service.
• If you press the blue padlock icon next to the Throw Distance value so that the
icon shows a Lock symbol, then moving the Zoom Slider will only adjust the Image Size bigger or smaller as would be visually represented if
you turned the Zoom Lens ring on your projector’s zoom lens to make the image bigger or smaller.
• If you click the padlock next to the Image Size
value so that the icon shows a Lock symbol, then moving the Zoom Slider will only adjust the Throw Distance position of the projector

As you move a projector
away from the screen or wall, the image will get bigger, and as you push the projector closer to the screen or wall the image will be smaller. To properly
fit your image onto a screen you need a projection calculator tool or throw chart to tell you the image size dimensions at the corresponding
throw distance. The binomial probability calculator will calculate a probability based on the binomial probability formula.

## What is a Binomial Probability?

Share your comments and suggestions with us on the Projection Calculator Pro. Our online calculators, converters, randomizers, and content are provided “as is”, free of charge, and without any warranty or guarantee. Each tool is carefully developed and rigorously tested, and our content is well-sourced, but despite our best effort it is possible they contain errors. We are not to be held responsible for any resulting damages from proper or improper use of the service. If your selected projector has a Zoom Lens then the projector’s Throw Distance or Image Size can be finely adjusted by moving the
Zoom Lens ring on your projector. The Zoom Range slider in the calculator will help you calculate the changes made by a Zoom Lens.

The above is a randomly generated binomial distribution from 10,000 simulated binomial experiments, each with 10 Bernoulli trials with probability of observing an event of 0.2 (20%). On
the graphical representation of a projector in the middle of the calculator, you will see dimension lines that will tell you the Throw Distance
measurement between the front of the projector lens and the surface of your wall or screen. On the graphical representation of a screen in the middle of the
calculator, you will see dimension lines that will tell you the height, width, and diagonal measurements of your image. The inverse function is required when computing the number of trials required to observe a certain number of events, or more, with a certain probability. For this we use the inverse normal distribution function which provides a good enough approximation. The calculator will find the simple and cumulative probabilities, as well as the mean, variance, and standard deviation of the binomial distribution.