Understanding Binomial and Poisson Distributions

What is the formula for the Binomial Distribution?

What is the formula for the Poisson Distribution?

Which of the following is an application of the Binomial Distribution?

• Predicting the number of phone calls received in an hour

• Calculating the probability of getting a certain number of heads in coin tosses

• Estimating the average number of cars passing through a toll booth

• Modelling the decay of radioactive particles

Which of the following is an application of the Poisson Distribution?

• Determining the probability of a certain number of defective items in a batch

• Calculating the probability of winning a lottery

• Predicting the number of emails received per day

• Estimating the probability of drawing a red card from a deck

What is a key difference between Binomial and Poisson distributions in terms of probability?

• Binomial distribution is used for continuous data, while Poisson is for discrete data

• Binomial distribution requires a fixed number of trials, while Poisson does not

• Poisson distribution is used for data with two possible outcomes, while Binomial is not

• Binomial distribution is used for rare events, while Poisson is not

Which real-world example can be modelled using the Binomial Distribution?

• The number of earthquakes in a year

• The number of students passing an exam

• The number of cars arriving at a service station

• The number of raindrops falling in a square metre

Which real-world example can be modelled using the Poisson Distribution?

• The number of heads in 10 coin flips

• The number of students in a classroom

• The number of phone calls received at a call centre

• The number of apples in a basket

• The number of successes

• The probability of success

• The number of trials

• The mean of the distribution

• The number of trials

• The probability of success

• The average rate of occurrence

• The number of successes

What is the main assumption of the Poisson Distribution?

• The events are dependent

• The events occur at a constant rate

• The number of trials is fixed

• The probability of success is constant