Table of contents
- 1. Intro to Stats and Collecting Data55m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically1h 45m
- 4. Probability2h 16m
- 5. Binomial Distribution & Discrete Random Variables2h 33m
- 6. Normal Distribution and Continuous Random Variables1h 38m
- 7. Sampling Distributions & Confidence Intervals: Mean1h 3m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- 9. Hypothesis Testing for One Sample1h 1m
- 10. Hypothesis Testing for Two Samples2h 8m
- 11. Correlation48m
- 12. Regression1h 4m
- 13. Chi-Square Tests & Goodness of Fit1h 20m
- 14. ANOVA1h 0m
5. Binomial Distribution & Discrete Random Variables
Poisson Distribution
Struggling with Statistics?
Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
A quality control inspector at a textile factory is examining long rolls of fabric for defects. The inspector knows from past experience that, on average, there are 0.5 defects per meter of fabric. What is the probability that the inspector finds 0 defects in any given meter of fabric?
A
B
C
D

1
Recognize that this problem involves a Poisson distribution, which is used to model the number of events (defects) occurring in a fixed interval (1 meter of fabric) when the events occur independently and at a constant average rate.
The formula for the Poisson probability is P(X = k) = (λ^k * e^(-λ)) / k!, where λ is the average rate of occurrence (0.5 defects per meter in this case), k is the number of events (0 defects here), and e is the base of the natural logarithm (approximately 2.718).
Substitute the given values into the formula: λ = 0.5 and k = 0. This gives P(X = 0) = (0.5^0 * e^(-0.5)) / 0!.
Simplify the terms: 0.5^0 equals 1, 0! (factorial of 0) equals 1, and e^(-0.5) is the exponential function evaluated at -0.5.
Combine the simplified terms to calculate the probability: P(X = 0) = (1 * e^(-0.5)) / 1. This gives the final probability of finding 0 defects in 1 meter of fabric.
Watch next
Master Introduction to the Poisson Distribution with a bite sized video explanation from Patrick
Start learningRelated Videos
Related Practice