Probability Distribution Practice

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What is a normal distribution?

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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 mean in a probability distribution?

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The mean is the average of all data points in a distribution, calculated by summing all values and dividing by the number of values.

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What is standard deviation?

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Standard deviation is a measure of the amount of variation or dispersion in a set of values. A low standard deviation means that the values tend to be close to the mean.

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What is the empirical rule in statistics?

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The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

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How do you calculate the interval for 95% of observations in a normal distribution?

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To find the interval for 95% of observations, use the formula: Mean ± 1.96 * Standard Deviation.

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What is a probability distribution?

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A probability distribution is a function that describes the likelihood of obtaining the possible values that a random variable can take.

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What is the difference between discrete and continuous probability distributions?

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Discrete probability distributions deal with countable outcomes (e.g., rolling a die), while continuous probability distributions deal with outcomes that can take any value within a range (e.g., measuring height).

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What is the binomial distribution?

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The binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.

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What is the formula for calculating the probability of getting exactly k successes in a binomial distribution?

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P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the probability of success.

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What does 'at most' mean in probability?

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'At most' refers to the maximum number of successes or occurrences in a given scenario, including all values up to that maximum.