1. An archer is able to hit the bull's-eye 57% of the time. If she shoots 12 arrows, what is the probability that she gets exactly 4 bull's-eyes? Assume each shot is independent of the others. Express your answer as a percentage rounded to the nearest hundredth without the % sign. 2. According to a college survey, 41% of all students work full time. Find the standard deviation for the number of students who work full time in samples of size 219 (rounded to the nearest hundredth). 3. According to a college survey, 66% of all students work full time. Find the mean for the number of students who work full time in samples of size 93 (rounded to the nearest hundredth). 4. A survey for brand recognition is done and it is determined that 66% of consumers have heard of Dull Computer Company. A survey of 16 randomly selected consumers is to be conducted. For such groups, would it be significantly high to get 14 consumers who recognize the Dull Computer Company name? Why or why not? Explain your answer using descriptive statistics and/or probability appropriately. If your reasoning requires a z-score, enter the z-score rounded to the nearest hundredth. If your reasoning requires a probability, enter the probability as a decimal rounded to the nearest ten-thousandth. 5. A naturalist leads whale watch trips every morning in March. The number of whales seen has a Poisson distribution with a mean of 1.97. Find the probability that on a randomly selected trip, the number of whales seen is 5. Express your answer as a percentage rounded to the nearest hundredth. 6. Suppose the probability of contracting a certain disease is 1 in 64 for a new case in a given year. Approximate the probability that in a town of 238 people there will be at least one new case of the disease next year. Express your answer as a percentage rounded to the nearest hundredth without the % sign. 7. In a binomial experiment with p=.35, what is P(exactly 5 successes in 7 trials)? (Express your answer as a decimal rounded to the nearest ten-thousandth.) 8. In a binomial experiment, if p=.46, what is q? 9. In a binomial experiment, if q=.249, what is p? 10. When estimating a binomial distribution with a Poisson distribution, if n=450 and p=.02, what is ? 11. In a discrete probability distribution, the probability values may be any number as long as the total of all the probabilities is exactly 1. True/False 12. In a binomial probability distribution, the probability of success will always be 50% since there are only two outcomes, success and failure. True/False 13. The mean of a probability distribution will always be one of the possible outcomes in the sample space for the experiment. True/False 14. Spinning a roulette wheel 12 times and recording the number that comes up on each spin is an example of a binomial experiment. True/ False 15. Spinning a roulette wheel 12 times and recording whether the outcome is odd or not on each spin is an example of a binomial experiment. True/false 16. The table below is a discrete probability distribution in which x represents the number of students that a statistics tutor may see on any given day and P(x) represents the probability that the tutor sees that number of students. x 0 1 2 3 4 5 P(x) 0.11 0.18 0.36 0.16 0.14 0.05 Why is this a discrete probability distribution? (Hint: Three answers are correct.) Options "x" is an unknown and its values are associated with corresponding random values. The sum of all probabilities is at most 1. Each probability value is positive. The sum of all probabilities is at least 1. "x" is an unknown and its values are associated with corresponding probabilities. Each probability value is between 0 and 1 inclusive. "x" is a numerical random variable and its values are associated with corresponding random values. The sum of all probabilities is 1. "x" is a numerical random variable and its values are associated with corresponding probabilities. Each probability value is non-negative. 17. The table below is a discrete probability distribution in which x represents the number of students that a statistics tutor may see on any given day and P(x) represents the probability that the tutor sees that number of students. x 0 1 2 3 4 5 P(x) 0.11 0.18 0.36 0.16 0.14 0.05 What is the mean of this discrete probability distribution? (Round to the nearest hundredth.) 18. The table below is a discrete probability distribution in which x represents the number of students that a statistics tutor may see on any given day and P(x) represents the probability that the tutor sees that number of students. x 0 1 2 3 4 5 P(x) 0.11 0.18 0.36 0.16 0.14 0.05 What is the variance of this discrete probability distribution? (Round to the nearest ten-thousandth.) 19. The table below is a discrete probability distribution in which x represents the number of students that a statistics tutor may see on any given day and P(x) represents the probability that the tutor sees that number of students. x 0 1 2 3 4 5 P(x) 0.11 0.18 0.36 0.16 0.14 0.05 What is the standard deviation of this discrete probability distribution? (Round to the nearest ten-thousandth.) 20. The table below is a discrete probability distribution in which x represents the number of students that a statistics tutor may see on any given day and P(x) represents the probability that the tutor sees that number of students. x 0 1 2 3 4 5 P(x) 0.11 0.18 0.36 0.16 0.14 0.05 What is the probability that a tutor sees at least two students on any given day? (Express your answer as a decimal rounded to the nearest hundredth.) 21. The table below is a discrete probability distribution in which x represents the number of students that a statistics tutor may see on any given day and P(x) represents the probability that the tutor sees that number of students. x 0 1 2 3 4 5 P(x) 0.11 0.18 0.36 0.16 0.14 0.05 What is the probability that a tutor sees at either four or five students on any given day? (Express your answer as a decimal rounded to the nearest hundredth.) 22. The table below is a discrete probability distribution in which x represents the number of students that a statistics tutor may see on any given day and P(x) represents the probability that the tutor sees that number of students. x 0 1 2 3 4 5 P(x) 0.11 0.18 0.36 0.16 0.14 0.05 What is the probability that a tutor sees exactly six students on any given day? (Express your answer as a decimal rounded to the nearest hundredth.) 23. A recent survey by the American Automobile Association revealed that 80% of teenage girls text while driving. You have been hired for a safety presentation to a high school class of 100 teenage girls. What is the mean number of girls in this class who text while driving? 24. A recent survey by the American Automobile Association revealed that 80% of teenage girls text while driving. You have been hired for a safety presentation to a high school class of 100 teenage girls. What is the variance of the number of girls in this class who text while driving? 25. A recent survey by the American Automobile Association revealed that 80% of teenage girls text while driving. You have been hired for a safety presentation to a high school class of 100 teenage girls. What is the standard deviation of the number of girls in this class who text while driving? 26. A recent survey by the American Automobile Association revealed that 80% of teenage girls text while driving. You have been hired for a safety presentation to a high school class of 100 teenage girls. What is the probability that exactly 75 of these girls text while driving? (Express your answer as a decimal rounded to the nearest ten-thousandth.) 27. A recent survey by the American Automobile Association revealed that 80% of teenage girls text while driving. You have been hired to for a safety presentation to a high school class of 100 teenage girls. Using technology (e.g. STATDISK), what is the probability that at least 85 of these girls text while driving? (Express your answer as a decimal rounded to the nearest ten-thousandth.) 28. A recent survey by the American Automobile Association revealed that 80% of teenage girls text while driving. You have been hired to for a safety presentation to a high school class of 100 teenage girls. Using technology (e.g. STATDISK), what is the probability that fewer than 70 of these girls text while driving? (Express your answer as a decimal rounded to the nearest ten-thousandth.) 29. Approximate the probability of getting 2 successes in 500 trials when p=.005? Hint: Check if the Poisson approximation can be used. (Express your answer as a decimal rounded to the nearest ten-thousands)