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FTCE Middle Grades Math: Probability Distributions Chapter Exam

Exam Instructions:

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

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Question 1 1. A student wants to compute the expected value of a continuous probability distribution describing the heights of a population of bears. Which of the following would she use?

Question 2 2. Suppose you toss three coins, what is the probability you get three heads?

Question 3 3. Why would height be defined by a continuous random variable?

Question 4 4. Consider the following probability distribution (see table below) of the number of firearms in a household, constructed from a survey of 25,000 randomly selected households. Let X = the number of firearms in a household, and assume that the probability of a household having more than 6 firearms in the home is negligible. If a household is selected at random, then how many firearms would you expect them to have?

Question 5 5. You conduct an experiment where you want to measure the number of rolls it takes to get two 6's in a row when you roll a fair six-sided die. State whether the random variable is discrete or continuous and give a summary of its values.

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Question 6 6. What variable represents the probability of success on an individual trial?

Question 7 7. To compute the expected value of a discrete probability distribution, which of the following is used?

Question 8 8. Asia is conducting an experiment for her psychology class. She asks 80 students if they believe in hypnosis. Previous studies show that 60% of the population believes in hypnosis. Based on the expected value, how many people should answer yes, they do believe in hypnosis, in Asia's study?

Question 9 9. What do we call a graph of probabilities associated with all the possible values taken by a continuous random variable?

Question 10 10. An agency decides to conduct a survey on household incomes in their county. Let x = the household income. What type of variable is x?

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Question 11 11. Which of the following is TRUE regarding the expected value associated with the probability density function?

Question 12 12. Suppose you play a game where you spin a spinner (see picture below) with areas of the colors on the spinner broken down as shown: 10% blue, 60% green, and 30% red. In addition, if the spinner lands on red you win 6 points, if it lands on blue you win 1 point, and if it lands on green you lose 5 points. If you keep spinning, how many points can you expect to win or lose per game?

Question 13 13. A person is rolling a die, and records the outcome of each roll. Which type of random variable captures this situation? Why?

Question 14 14. A television channel conducts a study on the number of TVs per household in their service area. Out of 1000 households surveyed, 350 have one TV, 500 have two TVs, 120 have three TVs and 30 have four TVs. How many TVs does each household have on average?

Question 15 15. From mortality tables it has been determined that the probability of a 20-year old female non-smoker dying within the year is 0.0023. Suppose an insurance company wants to sell a $60,000 1-year term life insurance policy to a 20-year old non-smoking female. What should they charge for the policy to make a profit of $30 per policy?

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Question 16 16. Which of the following is NOT a property of a random variable?

Question 17 17. A roulette wheel has 38 slots labeled with the numbers 1 through 36 and then 0 and 00. Slots 1 through 36 are colored either red or black. There are 18 red and 18 black. Slots 0 and 00 are colored green (see picture). Suppose that for a bet of $1 on red, the casino will pay you $2 if the ball lands on a red slot (a net gain of $1), and otherwise you lose your dollar. What can you expect to win or lose in this game?

Question 18 18. For which of the following random processes would you define a discrete random variable?

Question 19 19. What variable represents the number of trials in an experiment?

Question 20 20. Which of the following is TRUE about continuous random variables?

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Question 21 21. Suppose a survey was conducted across the country regarding the number of firearms that people had in their households. If the sample size was 25,000 and 17,000 households reported that they had no firearms in their home, what would be the empirical probability that a randomly selected household had no firearms in their home?

Question 22 22. Suppose you toss a coin twice, what is the probability you get two heads in row?

Question 23 23. Suppose you toss three coins. What is the probability that you get two heads and one tail if the order in which you get them does not matter?

Question 24 24. From mortality tables it has been determined that the probability of a 20-year old male non-smoker dying within the year is 0.0035. Suppose an insurance company wants to sell a $50,000 1-year life insurance policy to a 20-year old non-smoking male. What should they charge for the policy to break even?

Question 25 25. What do we call data that cannot be divided, which is distinct, and can only occur in certain values?

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Question 26 26. Which of the following situations is best modeled by a discrete random variable?

Question 27 27. You play a game where you toss a coin. On each toss if it lands with heads up, you win $1. However, if it lands with tails up, you lose $2. If you continue to play this game, how much can you expect to win or lose per game?

Question 28 28. Suppose a survey was conducted across the country regarding the number of firearms that people had in their households. Let X = the number of firearms in a household. From the survey of 30,000 households it was determined that the empirical probability of X = 1 was 0.2. How many of the households in the survey had one firearm in their home?

Question 29 29. A roulette wheel has 38 slots labeled with the numbers 1 through 36 and then 0 and 00. Slots 1 through 36 are colored either red or black. There are 18 red and 18 black. Slots 0 and 00 are colored green (see picture). On one spin of the roulette wheel, what is the probability that the ball lands on a red slot?

Question 30 30. Solving for the expected value of a continuous probability distribution involves which of the following?

FTCE Middle Grades Math: Probability Distributions Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

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