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Binomial Distribution vs. Poisson Distribution vs. Hypergeometric Probability

Related Topics

Wize University Statistics Textbook > Discrete Probability Distributions

Poisson Distribution

5 Activities

Wize University Statistics Textbook > Discrete Probability Distributions

Hypergeometric Probability

5 Activities

Wize University Statistics Textbook > Discrete Probability Distributions

Binomial Distribution

8 Activities

Binomial [B], Poisson [P], or Hypergeometric [H]? Enter B, P, or H in the boxes below.
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 and Poisson Distributions
At a dangerous intersection, 2.5% of cars drive through a red light. Suppose 100 cars drove by.
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 Hypergeometric Probability Questions:
Hypergeometric probability
In a box there are 5 gold, 3 silver, and 2 bronze balls. Three balls are drawn without replacement.
Determine the probability that at least one ball selected is silver.
Hypergeometric Distribution
There are seven people in Molly’s family -- 4 women and 3 men. If I select three of them at random, what is the probability that I will get exactly two men and one woman?
Hypergeometric Probability
The farm has 15 chickens, 7 cows, and 3 pigs. Which of the following is based on a hypergeometric distribution?
Hypergeometric Probability
Twin Pines is a small neighborhood with 157 houses. A “success” is when a home has the OWN channel, and the probability of success is known. A sample is drawn without replacement. Which model is most the appropriate?
Hypergeometric probability
There are 10 keys in front of you. One of the keys will open the prize car. If you get to pick three keys, what is the probability that one of them is the correct key?
Hypergeometric Probability
Ivan supervises night sift employees at Walmart. The Swine Flu is back and 15 of his night shift employees called in sick today. Ivan finds it odd that they all have Swine Flu and believes that some of them may be lying about their sickness to go to the Taylor Swift concert tonight.
An employee knows that of these 15 employees that called in sick, 6 have Taylor Swift concert tickets – but Ivan doesn’t know this! Ivan hires a private detective to randomly spy on 5 of his employees that called in sick. What is the probability that exactly 2 of the 5 selected employees will be caught with Taylor Swift tickets?
Statistical Properties: Practice
True or false? Enter "T" for true; "F" for false (without quotations).
Hypergeometric Probability
There are 8 buttons in front of you. Three of the buttons will set off the alarm. What is the probability that you will not set off the alarm after pressing 3 buttons?
Hypergeometric Probability Question
There are seven postdoctoral research fellows in Dr. Lemon’s lab – 4 women and 3 men. To be fair, she will select four of them at random to accompany her at a convention. What is the probability that she will get exactly two of each gender?
Hypergeometric Probability
There are 10 balls in a bag; 3 of them are gold balls. To win a prize, you must draw all three gold balls. You get to draw five balls. What is the probability you will win a prize?
Hypergeometric Probability
There are 6 pairs of socks in the dryer. Each pair has a different pattern. In other words, only one sock matches with another sock. You are in a hurry to class and randomly grabbed 4 individual socks from the dryer. What is the probability that all four socks have different patterns? (Relatable, right?)
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 and Poisson Distributions
At a dangerous intersection, 2.5% of cars drive through a red light. Suppose 100 cars drove by.
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.