Week 6 Binomial and Poisson Distributions

Question 1

What is the binomial distribution used for?

Answer 1

When you have a fixed number of independent trials, each with two possible outcomes (success or failure)

The binomial distribution is applicable in scenarios like flipping a coin multiple times or conducting a survey with yes/no responses.

Question 2

What type of distribution is used for rare events over a fixed interval?

Answer 2

Poisson distribution

The Poisson distribution is typically used for modeling the number of events in a fixed interval of time or space.

Question 3

What is the key parameter of the Poisson distribution?

Answer 3

Lambda (λ), which represents the average number of events in an interval

Lambda is crucial in defining the shape of the Poisson distribution.

Question 4

True or False: The normal distribution is symmetric and bell-shaped.

Answer 4

True

The normal distribution is characterized by its symmetry around the mean and its bell-like shape.

Question 5

What are the two parameters of a normal distribution?

Answer 5

Mean (μ) and standard deviation (σ)

These parameters determine the center and the spread of the normal distribution.

Question 6

Fill in the blank: The Central Limit Theorem states that the distribution of the sample means approaches a _______ distribution as the sample size increases.

Answer 6

normal

This theorem is fundamental in statistics because it justifies the use of normal distribution in many statistical procedures.

Question 7

What is the significance of the Central Limit Theorem in statistics?

Answer 7

It allows for the approximation of the sampling distribution of the sample mean by a normal distribution

This is particularly useful when dealing with large sample sizes, regardless of the original population distribution.