Binomial and Normal Distributions Review

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What is a continuous random variable?

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A continuous random variable is a variable that can take on an infinite number of values within a given range. For example, the time it takes for a student to complete an exam.

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What are the two main conditions for a probability distribution?

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1. All P(x) values must be between 0 and 1. 2. The sum of all P(x) values must equal 1.

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How do you calculate the mean of a binomial distribution?

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The mean (μ) of a binomial distribution is calculated using the formula μ = n * p, where n is the number of trials and p is the probability of success.

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What is the probability of a standard normal variable being at least a certain value?

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To find this probability, you can use the standard normal distribution table (Z-table) or a calculator to find the area to the right of that Z-score.

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What is the assumption of independence in a binomial distribution?

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In a binomial distribution, each trial must be independent, meaning the outcome of one trial does not affect the outcome of another.

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What is the formula for the variance of a binomial distribution?

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The variance (σ²) of a binomial distribution is calculated using the formula σ² = n * p * (1 - p), where n is the number of trials and p is the probability of success.

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What does it mean for a distribution to be normal?

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A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

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What is the standard deviation of a normal distribution?

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The standard deviation is a measure of the amount of variation or dispersion in a set of values. In a normal distribution, it determines the width of the curve.

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What is the significance of the area under the curve in a normal distribution?

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The area under the curve of a normal distribution represents the total probability, which equals 1. The area between two points represents the probability of a value falling within that range.

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What is a binomial experiment?

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A binomial experiment is a statistical experiment that has the following properties: a fixed number of trials, each trial has two possible outcomes (success or failure), and the probability of success is constant.