- Statistics Tutorial
- Home
- Adjusted R-Squared
- Analysis of Variance
- Arithmetic Mean
- Arithmetic Median
- Arithmetic Mode
- Arithmetic Range
- Bar Graph
- Best Point Estimation
- Beta Distribution
- Binomial Distribution
- Black-Scholes model
- Boxplots
- Central limit theorem
- Chebyshev's Theorem
- Chi-squared Distribution
- Chi Squared table
- Circular Permutation
- Cluster sampling
- Cohen's kappa coefficient
- Combination
- Combination with replacement
- Comparing plots
- Continuous Uniform Distribution
- Cumulative Frequency
- Co-efficient of Variation
- Correlation Co-efficient
- Cumulative plots
- Cumulative Poisson Distribution
- Data collection
- Data collection - Questionaire Designing
- Data collection - Observation
- Data collection - Case Study Method
- Data Patterns
- Deciles Statistics
- Dot Plot
- Exponential distribution
- F distribution
- F Test Table
- Factorial
- Frequency Distribution
- Gamma Distribution
- Geometric Mean
- Geometric Probability Distribution
- Goodness of Fit
- Grand Mean
- Gumbel Distribution
- Harmonic Mean
- Harmonic Number
- Harmonic Resonance Frequency
- Histograms
- Hypergeometric Distribution
- Hypothesis testing
- Interval Estimation
- Inverse Gamma Distribution
- Kolmogorov Smirnov Test
- Kurtosis
- Laplace Distribution
- Linear regression
- Log Gamma Distribution
- Logistic Regression
- Mcnemar Test
- Mean Deviation
- Means Difference
- Multinomial Distribution
- Negative Binomial Distribution
- Normal Distribution
- Odd and Even Permutation
- One Proportion Z Test
- Outlier Function
- Permutation
- Permutation with Replacement
- Pie Chart
- Poisson Distribution
- Pooled Variance (r)
- Power Calculator
- Probability
- Probability Additive Theorem
- Probability Multiplecative Theorem
- Probability Bayes Theorem
- Probability Density Function
- Process Capability (Cp) & Process Performance (Pp)
- Process Sigma
- Quadratic Regression Equation
- Qualitative Data Vs Quantitative Data
- Quartile Deviation
- Range Rule of Thumb
- Rayleigh Distribution
- Regression Intercept Confidence Interval
- Relative Standard Deviation
- Reliability Coefficient
- Required Sample Size
- Residual analysis
- Residual sum of squares
- Root Mean Square
- Sample planning
- Sampling methods
- Scatterplots
- Shannon Wiener Diversity Index
- Signal to Noise Ratio
- Simple random sampling
- Skewness
- Standard Deviation
- Standard Error ( SE )
- Standard normal table
- Statistical Significance
- Statistics Formulas
- Statistics Notation
- Stem and Leaf Plot
- Stratified sampling
- Student T Test
- Sum of Square
- T-Distribution Table
- Ti 83 Exponential Regression
- Transformations
- Trimmed Mean
- Type I & II Error
- Variance
- Venn Diagram
- Weak Law of Large Numbers
- Z table
- Statistics Useful Resources
- Statistics - Discussion

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

Poisson conveyance is discrete likelihood dispersion and it is broadly use in measurable work. This conveyance was produced by a French Mathematician Dr. Simon Denis Poisson in 1837 and the dissemination is named after him. The Poisson circulation is utilized as a part of those circumstances where the happening's likelihood of an occasion is little, i.e., the occasion once in a while happens. For instance, the likelihood of faulty things in an assembling organization is little, the likelihood of happening tremor in a year is little, the mischance's likelihood on a street is little, and so forth. All these are cases of such occasions where the likelihood of event is little.

Poisson distribution is defined and given by the following probability function:

${P(X-x)} = {e^{-m}}.\frac{m^x}{x!}$

Where −

${m}$ = Probability of success.

${P(X-x)}$ = Probability of x successes.

**Problem Statement:**

A producer of pins realized that on a normal 5% of his item is faulty. He offers pins in a parcel of 100 and insurances that not more than 4 pins will be flawed. What is the likelihood that a bundle will meet the ensured quality? [Given: ${e^{-m}} = 0.0067$]

**Solution:**

Let p = probability of a defective pin = 5% = $\frac{5}{100}$. We are given:

${n} = 100, {p} = \frac{5}{100} , \\[7pt]
\ \Rightarrow {np} = 100 \times \frac{5}{100} = {5}$

The Poisson distribution is given as:

${P(X-x)} = {e^{-m}}.\frac{m^x}{x!}$

Required probability = P [packet will meet the guarantee]

= P [packet contains up to 4 defectives]

= P (0) +P (1) +P (2) +P (3) +P (4)

$ = {e^{-5}}.\frac{5^0}{0!} + {e^{-5}}.\frac{5^1}{1!} + {e^{-5}}.\frac{5^2}{2!} + {e^{-5}}.\frac{5^3}{3!} +{e^{-5}}.\frac{5^4}{4!}, \\[7pt]
\ = {e^{-5}}[1+\frac{5}{1}+\frac{25}{2}+\frac{125}{6}+\frac{625}{24}] , \\[7pt]
\ = 0.0067 \times 65.374 = 0.438$

Advertisements