Probability Calculator Statistics

Probability Calculator:

\[ P(X) = \text{Probability calculation based on selected distribution} \]

Distribution Type:

Mean (μ):

Standard Deviation (σ):

X Value:

Number of Trials (n):

Success Probability (p):

Number of Successes (k):

Lambda (λ):

Number of Events (k):

Probability:

Unit Converter ▲

Unit Converter ▼

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1. What is Probability Calculator?

This calculator computes probabilities for various statistical distributions including normal, binomial, and Poisson distributions. It helps in determining the likelihood of events occurring under given parameters.

2. Supported Distributions

Normal Distribution: Continuous probability distribution characterized by bell-shaped curve.

\[ P(X) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2} \]

Binomial Distribution: Discrete probability distribution of successes in n independent trials.

\[ P(k) = C(n,k) p^k (1-p)^{n-k} \]

Poisson Distribution: Discrete probability distribution expressing probability of given number of events occurring in fixed interval.

\[ P(k) = \frac{\lambda^k e^{-\lambda}}{k!} \]

3. How to Use the Calculator

Steps:

Select the distribution type
Enter required parameters for the selected distribution
Click Calculate to get the probability

4. Applications

Uses: Statistical analysis, quality control, risk assessment, scientific research, and decision making under uncertainty.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between normal and binomial distributions?
A: Normal is continuous, binomial is discrete. Normal describes continuous data, binomial counts successes in trials.

Q2: When should I use Poisson distribution?
A: When modeling rare events occurring independently with known average rate (e.g., calls to call center, radioactive decay).

Q3: What does probability of 0.5 mean?
A: 50% chance of the event occurring (or 1 in 2 chance).

Q4: Can probability be greater than 1?
A: No, probabilities range from 0 (impossible) to 1 (certain).

Q5: How accurate are these calculations?
A: The calculations are mathematically exact for the given parameters, though real-world applications may have additional complexities.