Question
The binomial probability distribution is used with a discrete random variable. a continuous random variable. either a discrete or a continuous random variable, depending on the varianc either a discrete or a continuous random variable, depending on the sample
Ask by Hodges Bush. in the United States
Mar 10,2025
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Answer
The binomial probability distribution is used with a discrete random variable.
Solution
1. We start by recalling that a binomial distribution represents the number of successes in a fixed number of independent trials, where each trial is a Bernoulli trial (i.e., it has two outcomes, "success" or "failure").
2. Since the binomial random variable counts the number of successes, it takes on integer values from \(0\) to \(n\) (where \(n\) is the number of trials).
3. A random variable that takes on a countable set of values (in this case, integers) is a discrete random variable.
4. Therefore, the binomial probability distribution is used with a discrete random variable.
The correct answer is: a discrete random variable.
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The binomial probability distribution is all about discrete random variables! Think of it like flipping a coin a certain number of times; you're counting the number of heads (or any success) in those flips. This makes it ideal for scenarios where there are fixed trials, two possible outcomes, and a consistent probability of success on each trial. You might find the binomial distribution popping up in everyday situations, like determining the likelihood of getting a certain number of heads when tossing a coin 10 times or predicting how many customers will make a purchase after visiting a website. It's all about those yes-or-no results that stack up in fun ways!
