Prob Dist & Binomial

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What is the mean of a probability distribution?

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The mean (or expected value) of a probability distribution is the sum of all possible values, each multiplied by its probability. It represents the average outcome.

Tags

CCSS.HSS.MD.A.2

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How do you denote the probability of a random variable X being greater than or equal to a certain value?

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P(X ≥ k) denotes the probability that the random variable X is greater than or equal to k.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What is the probability of getting at least 4 correct answers on a 5-question true-false quiz?

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The probability of getting at least 4 correct answers is calculated using the binomial probability formula. For 4 correct answers, P(X=4) and for 5 correct answers, P(X=5) are summed.

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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.

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What is the condition for a valid probability distribution?

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A valid probability distribution must satisfy two conditions: 1) All probabilities must be between 0 and 1, and 2) The sum of all probabilities must equal 1.

Tags

CCSS.7.SP.C.7A

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How do you find the missing probability in a probability distribution?

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To find the missing probability, subtract the sum of the known probabilities from 1.

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What does P(X < k) represent?

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P(X < k) represents the probability that the random variable X takes on a value less than k.

Tags

CCSS.HSS.ID.A.4

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What is the binomial probability formula?

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The binomial probability formula is 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.

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What is the significance of the standard deviation in a probability distribution?

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The standard deviation measures the amount of variation or dispersion in a set of values. In a probability distribution, it indicates how spread out the values are around the mean.

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What does it mean if a probability distribution is skewed?

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A skewed probability distribution is one where the probabilities are not evenly distributed around the mean, leading to a longer tail on one side.