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Binomial and Poisson Distributions

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Wize University Statistics Textbook > Discrete Probability Distributions

Poisson Distribution

5 Activities

Wize University Statistics Textbook > Discrete Probability Distributions

Binomial Distribution

8 Activities

At a dangerous intersection, 2.5% of cars drive through a red light. Suppose 100 cars drove by.





More Poisson Distribution Questions:
Poisson Distribution
The average number of homes sold by Jon Jennings, a top realtor, is 14 homes per week. Assume he works all 7 days and all days are the same.
a) What is the probability that exactly 3 homes will be sold tomorrow?
b) What is the probability that at least 3 homes will be sold tomorrow?
Poisson Model
Andy is a rude bank teller. He gets an average of 3 complaints per 8-hour shift.
a) Determine the mean and standard deviation for the number of complaints in one hour.
b) What is the probability that he will get one complaint in the first hour?
Poisson Distribution
An injury is reported in Company A once a week. In Company B, an injury is reported only once a month. All injuries are reported and the occurrences of injuries in those companies are independent. In the next three weeks, what is the probability that Company A reports fewer than 2 injuries and Company B reports no injuries?
Let 1 month = 4 weeks
Binomial Distribution vs. Poisson Distribution vs. Hypergeometric Probability
Binomial [B], Poisson [P], or Hypergeometric [H]? Enter B, P, or H in the boxes below.
Poisson Distribution
Which of the following can be modelled with a Poisson distribution?
Poisson Distribution
A random variable X has a poisson distribution X ∼Poisson(2)X\ \sim Poisson\left(2\right). Find the probability that XX is at least 1.
Poisson distribution
An old apartment building experiences an average of 2 electrical failure a week. Determine the probability that there will be no electrical failure on a given day.
Poisson Distribution
The number of customers coming to Suzanne’s coffee shop has a mean of 6 customers per hour. What is the probability that at least one customer will come to her coffee shop in an interval of 30 minutes?
Poisson Distribution
Which of the following cannot be modelled with a Poisson distribution?
Poisson Distribution
Five paper cuts are reported to the HR manager each 7-day week, on average. What is the probability that at least one paper cut will be reported today?
Poisson distribution
The Moody Volcano in Hawaii erupts four times a year. What is the probability that it will not erupt in the next month?
Statistical Properties: Practice
True or false? Enter "T" for true; "F" for false (without quotations).
Poisson Distribution
Five injuries are reported at the gym each day. What is the probability that fewer than 3 injuries occur today?
More Binomial Distribution Questions:
Binomial RV
A student randomly guesses on 25  MC25\ \ MC questions, each with 44 options one of which is correct. Let XX represent the number of correctly guessed answers. Determine the value of E(X)E\left(X\right) and σ(𝑋)\sigma(𝑋).
Binomial Distribution
A survey showed the following:
20% of students sleep under 4 hours a night
15% of students sleep between 4 and 5 hours a night
Binomial Distribution
According to a self-conducted study, 60% of the socks in your friend Nitsy’s top drawer have a hole in them. Given a random sample of 20 socks from Nitsy’s top drawer, what is the expected number of them which have holes?
Binomial Distribution
According to studies, 75% of rabbits like carrots. If 14 rabbits are selected at random, what is the probability that more than 8 but fewer than 11 of them like carrots?
Binomial RV
13 cards are drawn from a standard deck with replacement. Let X represent the number of aces drawn. Find the variance of X, that isV(X).V(X).
Practice: Bernoulli Trials
When Ben asks a girl for her number, he gets it 20% of the time.
Binomial Distribution vs. Poisson Distribution vs. Hypergeometric Probability
Binomial [B], Poisson [P], or Hypergeometric [H]? Enter B, P, or H in the boxes below.
Binomial Probability
Leo can shoot a bull’s eye 60% of the time. He has 10 bullets.
a) What’s the probability that he will shoot a bull’s eye exactly 8 of the 10 times?
b) What’s the probability that he will shoot a bull’s eye at most 8 times?
Binomial Distribution
The probability that Todd makes a sale is 40%. He engaged with 50 customers today.
What is the probability that exactly half of the customers will buy something from him today?
Statistical Properties: Practice
True or false? Enter "T" for true; "F" for false (without quotations).
Binomial distribution
Samuel plays a game in which he wins a prize 20% of the time.
Discrete Random Variable
An ordinary die is rolled 164 times. Determine the expected number of times the die shows a number greater than four.
Binomial Distribution
The binomial mean is 90 and the binomial standard deviation is 6. Find nn.