Chapter 6 Review AP Statistics

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What is the mean of a random variable?

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The mean of a random variable is the average value it takes, calculated as the sum of all possible values multiplied by their probabilities.

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How do you calculate the mean of the total calories in a breakfast consisting of cereal and milk?

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To find the mean of the total calories (T), add the means of the individual components: Mean of T = Mean of cereal + Mean of milk = 110 + 140 = 250.

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What is the standard deviation of a random variable?

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The standard deviation measures the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean.

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How do you calculate the standard deviation of the total calories in a breakfast consisting of cereal and milk?

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What is the formula for calculating the mean of total revenue from a vending machine?

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Mean revenue (Y) = Price per bottle * Mean number of bottles sold. For example, if the price is $1.50 and the mean number of bottles is 50, then Mean Y = $1.50 * 50 = $75.

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What is the formula for calculating the standard deviation of total revenue from a vending machine?

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Standard deviation of revenue (Y) = Price per bottle * Standard deviation of number of bottles sold. If the price is $1.50 and the standard deviation is 15, then SD Y = $1.50 * 15 = $22.50.

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How do you calculate the probability of exceeding a certain number of cases in a binomial distribution?

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Use the binomial probability formula or normal approximation to find the probability of more than a certain number of successes. For example, if n = 17 and p = 0.4, calculate the probability of more than 10 cases.

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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 the number of trials and the probability of success.

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What is the Central Limit Theorem?

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The Central Limit Theorem states that the distribution of the sample mean will approach a normal distribution as the sample size increases, regardless of the original distribution of the population.