Chapter 4 test review

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What is the formula for calculating the standard deviation of a binomial distribution?

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The standard deviation (σ) of a binomial distribution is calculated using the formula: σ = √(n * p * (1 - p)), where n is the number of trials and p is the probability of success.

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What is a binomial distribution?

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A binomial distribution is a probability distribution that summarizes the likelihood that a value will take one of two independent states and is defined by two parameters: n (number of trials) and p (probability of success).

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How do you calculate the probability of getting exactly k successes in n trials in a binomial distribution?

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The probability of getting exactly k successes in n trials is calculated using the formula: P(X = k) = (n choose k) * p^k * (1 - p)^(n - k), where (n choose k) = n! / (k!(n-k)!).

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What is a continuous random variable?

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A continuous random variable is a variable that can take an infinite number of values within a given range. Examples include time, height, and weight.

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What is a discrete random variable?

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A discrete random variable is a variable that can take on a countable number of distinct values. Examples include the number of students in a class or the number of correct answers on a test.

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What is the probability of guessing correctly on a multiple-choice question with four options?

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The probability of guessing correctly on a multiple-choice question with four options is 1/4 or 0.25.

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How do you find the area of a rectangle?

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The area of a rectangle is found using the formula: Area = length × width.

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What is the expected value in probability?

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The expected value is the long-term average or mean of a random variable, calculated as E(X) = Σ [x * P(x)], where x is a value and P(x) is the probability of that value.

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What does it mean for a variable to be normally distributed?

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A variable is normally distributed if its probability distribution is symmetric about the mean, forming a bell-shaped curve.

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What is the significance of the standard deviation in statistics?

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The standard deviation measures the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.