Binomial Distribution

Question 1

What are the four things that you need in order to model something as a binomial distribution

Answer 1

1) The number of trials must be fixed.
2) Each trial must have only two possible outcomes.
3) The trials must be independent.
4) The probability of success must remain constant across trials.

Question 2

What is a binomial distribution?

Answer 2

A binomial distribution is a probability distribution that summarizes the likelihood of a value occurring in a given number of trials.

Question 3

How many conditions must be met to perform a binomial distribution?

Answer 3

Four conditions must be met.

Question 4

True or False: The trials in a binomial distribution must be dependent.

Answer 4

False.

Question 5

Fill in the blank: In a binomial distribution, each trial must have _____ outcomes.

Answer 5

two

Question 6

What does it mean for trials to be independent in a binomial distribution?

Answer 6

It means the outcome of one trial does not affect the outcome of another trial.

Question 7

True or False: The probability of success must remain constant in a binomial distribution.

Answer 7

True.

Question 8

Multiple Choice: Which of the following is NOT a condition for a binomial distribution? A) Fixed number of trials B) Independent trials C) Variable success probability D) Two outcomes per trial

Answer 8

C) Variable success probability

Question 9

Short Answer: Why is it important for trials to be independent in a binomial distribution?

Answer 9

It ensures that the outcome of one trial does not influence the others, allowing for accurate probability calculations.

Question 10

True or False: A binomial distribution can be used for scenarios with more than two outcomes.

Answer 10

False.

Question 11

What is an example of a binomial distribution scenario?

Answer 11

Flipping a coin a fixed number of times and counting the number of heads.

Question 12

Fill in the blank: In a binomial distribution, the probability of success is denoted by _____ and the probability of failure is denoted by _____ .

Answer 12

p, q (where q = 1 - p)

Question 13

What does ‘n’ represent in the context of a binomial distribution?

Answer 13

The fixed number of trials.

Question 14

Multiple Choice: If a binomial distribution has 10 trials and the probability of success is 0.5, what is the probability of getting exactly 5 successes? A) 0.246 B) 0.5 C) 0.5^10 D) 0.1

Answer 14

A) 0.246

Question 15

True or False: The number of trials can vary in a binomial distribution.

Answer 15

False.

Question 16

Short Answer: What happens if the probability of success changes during trials in a binomial distribution?

Answer 16

It violates the condition of constant probability, making it unsuitable for binomial distribution.

Question 17

What is the significance of having only two outcomes in a binomial distribution?

Answer 17

It simplifies the calculation of probabilities and allows for the use of specific formulas.

Question 18

Fill in the blank: The outcomes in a binomial distribution are often referred to as _____ and _____ .

Answer 18

success, failure

Question 19

Multiple Choice: Which of the following distributions can be used if the conditions for a binomial distribution are not met? A) Normal distribution B) Poisson distribution C) Exponential distribution D) Both A and B

Answer 19

D) Both A and B (however at A-Level we will only look at A)

Question 20

Short Answer: How does the number of trials affect the shape of the binomial distribution?

Answer 20

As the number of trials increases, the distribution approaches a normal distribution shape.