Binomial Distribution

Density Function

The density function of the (family of) Binomial distribution(s) is

The family depends on the parameters . For each new values of , there is a new member of the family and hence a new density function.

Choose values for and :

Examples

  1. 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?

  2. 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?

  3. 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 follows the Binomial distribution, ... WIP.

References