CHAPTER 5

Binomial and Poisson Probability Distributions

The Poisson Distribution

• Discrete

• Probability

• Distribution

• Binomial Distribution

Example 1:

• Suppose you take a 25 question multiple choice test where each question has 5 choices. This is the pop quiz from Hades that you had no clue was coming and have no clue as to the correct answers, so you randomly guess at each question.

• Is the scenario binomial

• Find the probability that you guess correctly at exactly 15 questions.

• Find the probability that you get at most 8 correct answers.

• Find the probability that you get at least 12 correct.

The Poisson Distribution

• Properties

• The PDF P(x)

Example 2:

• During a period of time phone-in registrations are taken at BCCC at the rate of one call every 2 minutes.

• a) find the expected number of calls in one hour

• b) find the probability of having 3 calls in a 5-minute period

• c) find the probability of at most 2 calls in 5 minutes

• d) find the probability of more than one call in 5 minutes

Example 3:

• Each year 450 accidental deaths due to firearms occur in the 15-24 age group

• a) find the average number of accidental deaths due to firearms in a typical week

• b) find the probability of no accidental deaths due to firearms in a typical week

• c) find the probability of 2 or more accidental deaths due to firearms in a typical day

Example 4:

• Household Information and Security Systems produces and installs 300 custom made home security units every week. The units are priced to include a one-day installation. A unit with either a design or production problem must be modified on site and will require more than 1 day to install. After an intensive self study of their records, HISS has found that if they are operating at standard quality, 10% of the units will have problems and require a second day to install. For quality control HISS samples 6 systems and records the number with problems. Find the probability that the number of security systems (out of 6) that require a second day of service will be …

• A) none

• B) at most 1

• C) less than 3