Binomial Basics
What are the two possible outcomes for each observation in a binomial distribution?
What is success or failure?
This condition states that each trial must have the same probability of success.
What is the constant probability condition?
This symbol represents the probability of success in a binomial distribution.
What is p?
What is 4! equal to?
What is 24?
This type of data has only two possible categories, like yes/no or male/female.
What is binary data?
What does the 'x' represent in a binomial distribution?
What is the number of successes in n trials?
This many conditions must be met for the binomial distribution to apply.
What is three?
If p is the probability of success, this expression gives the probability of failure.
What is 1-p?
By definition, 0! equals this value.
What is 1?
If 75% of adults have health insurance, this is the expected number of insured adults in a random sample of 200.
What is 150?
What does the 'p' represent in a binomial distribution?
What is probability of successes?
This condition means that the result of one trial does not affect the results of other trials.
What is independence?
The mean of a binomial distribution equals n times this value.
What is p?
Calculate 5! divided by 3!
What is 20?
(5! = 120, 3! = 6, so 120/6 = 20)
In a referendum where each voter independently votes yes with probability 0.55, this represents what x counts in the binomial distribution.
What is the number of 'yes' votes
How do I get to the binomial probability formula on the calculator?
What is 2nd VARS, Distribution, binompdf?
Name all three conditions required for the binomial distribution.
What are: binary data, same probability of success for each trial, and independent trials?
When a telemarketer has a 15% success rate and makes 25 calls per day, this is the most likely number of sales they'll make.
What is 3 or 4?
since np = 3.75
The expression n!/(x!(n-x)!) is called this in the binomial formula.
What is the binomial coefficient (or combination)?
If a basketball player makes 80% of her free throws, this is the probability she makes all 6 free throws in tonight's game.
What is 0.262?
If n=5 and p=0.3, calculate the mean and standard deviation of the binomial distribution.
What is μ = 1.5 and σ ≈ 1.025?
(μ = 5×0.3 = 1.5; σ = √(5×0.3×0.7) = √1.05 ≈ 1.025)
Explain why independence might be violated when sampling from a small population.
What is: when sampling without replacement from a small population, selecting one person changes the probability for the next selection?
For n=3 trials with p=0.5, calculate P(X=2).
What is 0.375 or 37.5%?
If n=10 and p=0.4, what is the expected number of successes and its standard deviation?
What is μ = 4 and σ ≈ 1.55?
(μ = 10×0.4 = 4; σ = √(10×0.4×0.6) = √2.4 ≈ 1.55)
For a quality control inspector checking 20 items where each has a 2% defect rate, this distribution models the number of defective items found.
Hint: What would the values of n & p be?
What is the binomial distribution with n=20 and p=0.02?