CHAPTER 5 Binomial and Poisson Probability Distributions.

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Presentation transcript:

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 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