Binomial Distribution Solution

STEP 0: Pre-Calculation Summary
Formula Used
Binomial Distribution = Number of Trials!*(Probability of Success of Single Trial^Specific Outcomes within Trials)*(Probability of Failure of Single Trial^(Number of Trials-Specific Outcomes within Trials))/(Specific Outcomes within Trials!*(Number of Trials-Specific Outcomes within Trials)!)
Pbinomial = ntrials!*(p^x)*(q^(ntrials-x))/(x!*(ntrials-x)!)
This formula uses 5 Variables
Variables Used
Binomial Distribution - The binomial distribution can be thought of as simply the probability of a Success or Failure outcome in an experiment or survey that is repeated multiple times.
Number of Trials - The Number of Trials is the number of times a certain probabilistic event is tried out multiple times.
Probability of Success of Single Trial - The Probability of Success of Single Trial is the favorable possibility of the outcome of a certain individual event.
Specific Outcomes within Trials - Specific Outcomes within Trials are the number of times a certain outcome takes place within a given set of trials.
Probability of Failure of Single Trial - The Probability of Failure of Single Trial is the favorable possibility of the outcome not happening for a certain individual event.
STEP 1: Convert Input(s) to Base Unit
Number of Trials: 7 --> No Conversion Required
Probability of Success of Single Trial: 0.6 --> No Conversion Required
Specific Outcomes within Trials: 3 --> No Conversion Required
Probability of Failure of Single Trial: 0.4 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Pbinomial = ntrials!*(p^x)*(q^(ntrials-x))/(x!*(ntrials-x)!) --> 7!*(0.6^3)*(0.4^(7-3))/(3!*(7-3)!)
Evaluating ... ...
Pbinomial = 0.193536
STEP 3: Convert Result to Output's Unit
0.193536 --> No Conversion Required
FINAL ANSWER
0.193536 <-- Binomial Distribution
(Calculation completed in 00.004 seconds)

Credits

Created by Suman Ray Pramanik
Indian Institute of Technology (IIT), Kanpur
Suman Ray Pramanik has created this Calculator and 50+ more calculators!
Verified by Akshada Kulkarni
National Institute of Information Technology (NIIT), Neemrana
Akshada Kulkarni has verified this Calculator and 900+ more calculators!

12 Industrial Parameters Calculators

Binomial Distribution
Go Binomial Distribution = Number of Trials!*(Probability of Success of Single Trial^Specific Outcomes within Trials)*(Probability of Failure of Single Trial^(Number of Trials-Specific Outcomes within Trials))/(Specific Outcomes within Trials!*(Number of Trials-Specific Outcomes within Trials)!)
Normal Distribution
Go Normal Distribution = e^(-(Specific Outcomes within Trials-Mean of Distribution)^2/(2*Standard Deviation of distribution^2))/(Standard Deviation of distribution*sqrt(2*pi))
Learning Factor
Go Learning Factor = (log10(Time for Task 1)-log10(Time for n Tasks))/log10(Number of Tasks)
Poisson Distribution
Go Poisson Distribution = Mean of Distribution^(Specific Outcomes within Trials)*e^(-Mean of Distribution)/(Specific Outcomes within Trials!)
Annual Devaluation Rate
Go Annual Devaluation Rate = (Rate of Return Foreign Currency-Rate of Return USD)/(1+Rate of Return USD)
Crashing
Go Cost Slope = (Crash Cost-Normal Cost)/(Normal Time-Crash Time)
Forecasting Error
Go Forecasting Error = Observed Value at Time t-Smooth Averaged Forecast for Period t
Macroscopic Traffic Density
Go Traffic Density in vpm = Hourly Flow Rate in vph/(Avg. Travel Speed/0.277778)
General Sewing Data
Go GSD = (Man Power*Work Hours)/Target
Traffic Intensity
Go Traffic Intensity = Mean Arrival Rate/Mean Service Rate
Variance
Go Variance = ((Pessimistic Time-Optimistic Time)/6)^2
Reorder Point
Go Reorder Point = Lead Time Demand+Safety Stock

Binomial Distribution Formula

Binomial Distribution = Number of Trials!*(Probability of Success of Single Trial^Specific Outcomes within Trials)*(Probability of Failure of Single Trial^(Number of Trials-Specific Outcomes within Trials))/(Specific Outcomes within Trials!*(Number of Trials-Specific Outcomes within Trials)!)
Pbinomial = ntrials!*(p^x)*(q^(ntrials-x))/(x!*(ntrials-x)!)

What is binomial distribution?

The binomial distribution can be thought of as simply the probability of a Success or Failure outcome in an experiment or survey that is repeated multiple times. The binomial distribution is a probability distribution that summarizes the likelihood that a value will take one of two independent values under a given set of parameters or assumptions.

How to Calculate Binomial Distribution?

Binomial Distribution calculator uses Binomial Distribution = Number of Trials!*(Probability of Success of Single Trial^Specific Outcomes within Trials)*(Probability of Failure of Single Trial^(Number of Trials-Specific Outcomes within Trials))/(Specific Outcomes within Trials!*(Number of Trials-Specific Outcomes within Trials)!) to calculate the Binomial Distribution, The binomial distribution can be thought of as simply the probability of a Success or Failure outcome in an experiment or survey that is repeated multiple times. Binomial Distribution is denoted by Pbinomial symbol.

How to calculate Binomial Distribution using this online calculator? To use this online calculator for Binomial Distribution, enter Number of Trials (ntrials), Probability of Success of Single Trial (p), Specific Outcomes within Trials (x) & Probability of Failure of Single Trial (q) and hit the calculate button. Here is how the Binomial Distribution calculation can be explained with given input values -> 0.193536 = 7!*(0.6^3)*(0.4^(7-3))/(3!*(7-3)!).

FAQ

What is Binomial Distribution?
The binomial distribution can be thought of as simply the probability of a Success or Failure outcome in an experiment or survey that is repeated multiple times and is represented as Pbinomial = ntrials!*(p^x)*(q^(ntrials-x))/(x!*(ntrials-x)!) or Binomial Distribution = Number of Trials!*(Probability of Success of Single Trial^Specific Outcomes within Trials)*(Probability of Failure of Single Trial^(Number of Trials-Specific Outcomes within Trials))/(Specific Outcomes within Trials!*(Number of Trials-Specific Outcomes within Trials)!). The Number of Trials is the number of times a certain probabilistic event is tried out multiple times, The Probability of Success of Single Trial is the favorable possibility of the outcome of a certain individual event, Specific Outcomes within Trials are the number of times a certain outcome takes place within a given set of trials & The Probability of Failure of Single Trial is the favorable possibility of the outcome not happening for a certain individual event.
How to calculate Binomial Distribution?
The binomial distribution can be thought of as simply the probability of a Success or Failure outcome in an experiment or survey that is repeated multiple times is calculated using Binomial Distribution = Number of Trials!*(Probability of Success of Single Trial^Specific Outcomes within Trials)*(Probability of Failure of Single Trial^(Number of Trials-Specific Outcomes within Trials))/(Specific Outcomes within Trials!*(Number of Trials-Specific Outcomes within Trials)!). To calculate Binomial Distribution, you need Number of Trials (ntrials), Probability of Success of Single Trial (p), Specific Outcomes within Trials (x) & Probability of Failure of Single Trial (q). With our tool, you need to enter the respective value for Number of Trials, Probability of Success of Single Trial, Specific Outcomes within Trials & Probability of Failure of Single Trial and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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