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AP Stats/Stats Fall Final Review 2 Name: AP or Stats Topic 11: Probability Vocabulary: Probability Simulation Complement of an Event Law of Large Numbers 1. The probability that a randomly selected student passes the AP exam is 0.57. What is the probability of the complement of this event? 2. Juan is a tennis player. He claims that he gets 73% of first serves into play. In his most recent match, Juan missed 6 out of 10 of his first serves. Assuming Juan’s claim is true, would it be surprising for Juan to miss 60% of his first serves? Describe and carry out a simulation to estimate the probability that Juan would miss 6 or more out of 10 of his first serves. Perform 10 trials of the simulation. Line Topic 12: Conditional probability Vocabulary: Independent events Conditional probability Venn diagram 3.Are STEM high school students, per grade level, more likely to attend a football game than not? 26% of STEM high school students are seniors, 24% are juniors, 19% are sophomores and 31% are freshman. The probability that a student is a senior and attends a football game is 4%. The probability that a student is a junior and attends a football game is 5%. The probability that a student is a sophomore and attends a football game is 3%. And finally, the probability that a student is a freshman and attends a game is 2%. Draw a tree diagram to depict this scenario. (a) What is the probability that a randomly selected student does not attend football games? 1

AP Stats/Stats Fall Final Review 2 Name: AP or Stats (b) Given that a randomly selected student does not attend a football game, what is the probability they are a senior? (c) Given that a randomly selected student is not a senior, what is the probability that they attend a football game? (d) Given that a randomly selected student is not a sophomore, what is the probability that they will not attend a football game? Topic 13: Random Variable Vocabulary: Random Variable Probability distribution 4. We will let X be the number of girls in a four-child family. We will assume that the probability of having a girl is 0.5. Here is the probability distribution for X. (a) What is the expected number of girls born in a four-child family? Show your work. (b) What is the standard deviation of the number of girls born in a four-child family? Show your work. (c) Interpret the expected value and standard deviation of the number of girls born in a four-child family. Topic 14: Combining and transforming random variables Vocabulary: How to calculate the mean and standard deviation of the sum of two random variables How to calculate the mean and standard deviation of the difference of two random variables How does adding/subtracting a constant to a random variable affect its mean and standard deviation How does multiplying/dividing a constant to a random variable affect its mean and standard deviation 5. The average salary for teachers in Orange County is $43,787 with a standard deviation of $4800. The school board decides to be generous for once and give all teachers holiday a bonus of 500 plus an additional retention bonus equal to 10 percent of their salary. What is the mean and standard deviation of the bonus the teachers will receive? 6. The local Toyota dealership pays an average of $9,260 with a standard deviation of $1099 for used car trade-ins. They sell new cars at an average of $28,451 with a standard deviation of $3392. Assume independence of new car and trade-ins. What are the mean and standard deviation of the revenue this dealership should expect when a person trades in a car and purchases a new one? 2

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