WorksheetsGeometric and Binomial Distributions
Total questions: 15
Worksheet time: 45mins
What are the parameters of a Binomial Distribution?
The number of trials (n) and the probability of success (p) in each trial.
The mean (μ) and standard deviation (σ) of the distribution.
The total number of successes and failures in the trials.
The variance (σ²) and the skewness of the distribution.
What is the mean of a Binomial Distribution?
μ = n * p
μ = n + p
μ = n / p
μ = p / n
What is the formula for the probability of exactly k successes in a Binomial Distribution?
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
P(X = k) = (n choose k) * (1-p)^k * p^(n-k)
P(X = k) = p^k * (1-p)^n
P(X = k) = n * p * (1-p)^(n-1)
What is a Binomial Distribution?
A probability distribution that summarizes the likelihood that a value will take on one of two independent outcomes over a specified number of trials.
A distribution that describes the probability of a continuous random variable.
A statistical method used to analyze the relationship between two variables.
A type of distribution that only applies to normal data sets.
What is the standard deviation of the number of beach goers who get sunburned in a survey of 75 beach goers?
3.50
4.04
5.25
2.80
What is the assumption of success/failure in Binomial Distribution?
Each trial must result in a success or a failure, with no other outcomes.
Each trial can result in multiple outcomes.
The probability of success must be greater than the probability of failure.
The trials must be independent but can have varying outcomes.
What does 'n choose k' mean in the context of Binomial Distribution?
It represents the number of ways to choose k successes from n trials, calculated as n! / (k!(n-k)!).
It indicates the probability of getting exactly k successes in n trials.
It is a method to calculate the mean of a binomial distribution.
It represents the total number of trials in a binomial experiment.
What is the standard deviation of a Binomial Distribution?
σ = √(n * p * (1 - p))
σ = n * p
σ = p * (1 - p)
σ = √(n + p)
What is the significance of the Central Limit Theorem in relation to Binomial Distribution?
As n becomes large, the Binomial Distribution approaches a normal distribution, allowing for easier calculations.
The Central Limit Theorem states that all distributions are normal regardless of sample size.
The Central Limit Theorem only applies to continuous distributions, not discrete ones like the Binomial.
The Binomial Distribution remains unchanged regardless of the sample size.
What is a Geometric Distribution?
A probability distribution that models the number of trials needed for the first success in a series of independent Bernoulli trials.
A distribution that describes the probability of a given number of successes in a fixed number of trials.
A distribution that represents the likelihood of a single event occurring in a given time frame.
A distribution that models the time until the next event occurs in a Poisson process.
What is the probability of answering exactly 70 questions correctly out of 100 with a 90% success rate?
P(X = 70) = (100 choose 70) * (0.90)^70 * (0.10)^30
P(X = 70) = (100 choose 70) * (0.80)^70 * (0.20)^30
P(X = 70) = (100 choose 70) * (0.70)^70 * (0.30)^30
P(X = 70) = (100 choose 70) * (0.60)^70 * (0.40)^30
What is the mean number of beach goers who get sunburned if 32% of 75 beach goers get sunburned?
20
22
24
26
What is the probability of getting exactly 2 successes in 20 trials with a success probability of 0.11?
0.282
0.150
0.350
0.200
What is the assumption of independence in Binomial Distribution?
Each trial must be independent, meaning the outcome of one trial does not affect the others.
The trials must be dependent on each other to ensure accurate results.
The number of trials must be fixed and cannot change during the experiment.
The probability of success must remain constant across all trials.
What is the difference between Binomial and Geometric Distributions?
Binomial Distribution counts the number of successes in a fixed number of trials, while Geometric Distribution counts the number of trials until the first success.
Both distributions count the number of successes in an infinite number of trials.
Binomial Distribution is used for continuous data, while Geometric Distribution is used for categorical data.
Geometric Distribution counts the number of successes in a fixed number of trials, while Binomial Distribution counts the number of trials until the first success.
