Stat Review

What is a random variable?

• A random variable is a fixed value that never changes.

• A random variable is a variable whose possible values are outcomes of a random phenomenon.

• A random variable is a variable that is always predictable.

• A random variable is a variable that only takes on one value.

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Define probability distribution.

• A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment or random process.

• A probability distribution is a type of car engine

• A probability distribution is a weather forecast model

• A probability distribution is a cooking recipe

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Explain the concept of mathematical expectations.

• Mathematical expectations are calculated by adding all outcomes without considering their probabilities.

• The concept of mathematical expectations involves calculating the average value of a random variable by multiplying each outcome by its probability and summing them up.

• Mathematical expectations involve dividing each outcome by its probability to find the average value of a random variable.

• The concept of mathematical expectations is only applicable to discrete random variables.

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CCSS.HSS.MD.A.2

How is variance calculated in probability theory?

• Variance = Σ((x - μ)²) / n, where x is the range, μ is the mean, and n is the total number of data points.

• Variance = Σ((x - μ)²) / n, where x is the median, μ is the mean, and n is the total number of data points.

• Variance = Σ((x - μ)²) / n, where x is the mode, μ is the mean, and n is the total number of data points.

• Variance = Σ((x - μ)²) / n, where x is each data point, μ is the mean, and n is the total number of data points.

What is the expected value of a random variable?

• The expected value of a random variable is the sum of each possible value multiplied by its probability of occurring.

• The expected value of a random variable is the maximum of the possible values.

• The expected value of a random variable is the mode of the possible values.

• The expected value of a random variable is the median of the possible values.

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Describe the characteristics of a normal distribution.

• A normal distribution is always bimodal, with two distinct peaks in the data distribution.

• A normal distribution follows the 50-75-100 rule, where approximately 50% of the data falls within one standard deviation.

• A normal distribution is symmetric around its mean, with the majority of the data falling within one standard deviation of the mean. It follows the 68-95-99.7 rule, where approximately 68% of the data falls within one standard deviation, 95% within two standard deviations, and 99.7% within three standard deviations.

• A normal distribution is skewed to the left, with the majority of the data falling within one standard deviation of the mean.

What is the mean of a normal distribution?

• The mean of a normal distribution is equal to the standard deviation.

• The mean of a normal distribution is always zero.

• The mean of a normal distribution is always negative.

• The mean of a normal distribution is equal to the center of the distribution, which is represented by the peak of the bell curve.

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What is the standard deviation of a normal distribution?

• 4

• 2

• 3

• 1

How is the normal distribution used in real-life applications?

• The normal distribution is used to model various phenomena and understand probabilities in real-life applications.

• The normal distribution is only used in theoretical mathematics and has no practical applications.

• The normal distribution is only applicable to a limited number of fields and industries.

• The normal distribution is used to predict exact outcomes in real-life scenarios.

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Calculate the probability of a value falling within one standard deviation of the mean in a normal distribution.

• 0.95

• 0.50

• 0.33

• 0.68

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