Distributions Understanding

A factory produces light bulbs, and the probability that a bulb is defective is 0.05. If a random sample of 10 bulbs is selected, what is the probability that exactly 2 bulbs are defective? Use the binomial distribution formula.

• 0.0746

• 0.1029

• 0.0032

• 0.1938

Which of the following scenarios is best modeled by a geometric distribution?

• The number of defective items in a batch of 100.

• The number of phone calls received in an hour.

• The number of trials until the first success in a series of independent Bernoulli trials.

• The number of students in a classroom.

A call center receives an average of 5 calls per hour. What is the probability that exactly 3 calls are received in a given hour? Use the Poisson distribution formula.

• 0.1404

• 0.2650

• 0.1008

• 0.1804

Which distribution would you use to model the number of successes in a fixed number of independent Bernoulli trials?

• Poisson Distribution

• Geometric Distribution

• Binomial Distribution

• Normal Distribution

If the probability of success in a single trial is 0.2, what is the probability that the first success occurs on the 4th trial? Use the geometric distribution formula.

• 0.1024

• 0.1280

• 0.4096

• 0.2048

A bookstore sells an average of 3 rare books per week. What is the probability that they sell exactly 2 rare books in a week? Use the Poisson distribution formula.

• 0.2240

• 0.4232

• 0.1804

• 0.2241

Which of the following is a characteristic of the Poisson distribution?

• It models the number of successes in a fixed number of trials.

• It models the time until the first success.

• It models the number of events in a fixed interval of time or space.

• It models the probability of a single success.

A coin is flipped 8 times. What is the probability of getting exactly 3 heads? Use the binomial distribution formula.

• 0.2188

• 0.1445

• 0.2734

• 0.1094

Which distribution would you use to model the number of events occurring in a fixed interval of time or space?

• Binomial Distribution

• Geometric Distribution

• Poisson Distribution

• Exponential Distribution

If the probability of success in a single trial is 0.3, what is the probability that the first success occurs on the 5th trial? Use the geometric distribution formula.

• 0.0720

• 0.1029

• 0.0729

• 0.1020