Poisson Distribution Probability Problems

This video tutorial explains how to calculate the probability of a Poisson distribution using a real-world example. It involves determining the probability that a sample of 300 electric motors will have two or fewer defective units, given a defect rate of 0.01. The tutorial covers calculating the mean, applying the Poisson formula for different values of k, and evaluating the probability expression. The final result is presented as a percentage, providing a clear understanding of the process.

What type of distribution is used to model the probability of a given number of events happening in a fixed interval?

• Poisson distribution

• Normal distribution

• Binomial distribution

• Uniform distribution

In the given problem, what is the probability that an electric motor is defective?

• 0.02

• 0.10

• 0.01

• 0.05

How is the mean (mu) calculated for the Poisson distribution in this example?

• Sample size divided by defective rate

• Sample size minus defective rate

• Defective rate times sample size

• Defective rate divided by sample size

What is the mean (mu) value for the Poisson distribution in this problem?

• 2

• 1

• 3

• 4

What is the probability that the sample will contain two or fewer defective motors?

• Probability of x=2 only

• Probability of x=1 plus probability of x=2

• Probability of x=0 plus probability of x=1

• Probability of x=0 plus probability of x=1 plus probability of x=2

For the probability calculation of x=0, what is the value of k?

• 1

• 0

• 2

• 3

What is the formula used to calculate the probability for a specific value of x in a Poisson distribution?

• k^mu * e^-k / mu!

• k^mu * e^-mu / k!

• mu^k * e^-mu / k!

• mu^k * e^k / mu!

What is the probability of having exactly one defective motor in the sample?

• 3^3 * e^-3 / 3!

• 3^2 * e^-3 / 2!

• 3^1 * e^-3 / 1!

• 3^0 * e^-3 / 0!

What is the final probability that the sample contains two or fewer defective motors?

• 0.1234

• 0.6232

• 0.4232

• 0.5232

What percentage does the final probability of two or fewer defective motors represent?

• 32.32%

• 42.32%

• 62.32%

• 52.32%