Binomial Distribution
Density Function
The density function of the (family of) Binomial distribution(s) is
The family depends on the parameters
Choose values for
Examples
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Suppose an electronics manufacturing company produces microchips that are used in various electrical devices. Based on quality control tests, it's found that 95% of the microchips are free from defects, meaning they operate as expected. An electrical engineer randomly selects 10 microchips from the production line to use in a prototype device.
a. What is the probability that all 10 microchips selected are free from defects?
b. What is the probability that exactly 8 out of the 10 microchips selected are free from defects?
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A city has 50 bridges that need to be inspected for safety. From past data, it is known that any given bridge has a 10% chance of failing the inspection due to significant wear and tear.
a. What is the probability that exactly 5 bridges will fail the inspection?
b. What is the probability that at least 3 bridges will fail the inspection?
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At a certain school, 70% of students prefer chocolate ice cream over vanilla. If a random sample of 10 students is taken,
a. what is the probability that exactly 7 students prefer chocolate?
b. what is the probability that at least 8 students prefer chocolate?
Calculator
Suppose a random variable
References
- Poisson distribution. Wikipedia: The Free Encyclopedia. Wikimedia Foundation, Inc. Accessed 2023-06-10.