Fall 2014 Exam Score: /75

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1 Math 12 Fall 2014 Name Exam Score: /75 Total Class Percentage to Date Exam 2 For problems 1-6, circle the letter next to the response that BEST answers the question or completes the sentence. You do not have to show any work or write any explanations here. Make sure to read each statement carefully! each 1. The probability of an event is always A) equal to 1 B) between 0 and 1, inclusive C) between -1 and 1, inclusive D) a positive number 2. Two complementary events A) taken together do not include all outcomes for an experiment B) taken together include all outcomes for an experiment C) can occur together D) have the same probabilities 3. The number of ways one can select a 5 digit code ( if repetition of numbers is allowed) is 5 A) 10 B) 5! C) 10 C 5 D) 10 P 5 4. The correlation coefficients for the following data sets are: r = 0.34 r = 0.71 r = r = Plot A Plot B Plot C Plot D The correlation coefficient for Plot A is A) r = 0.34 B) r = 0.71 C) r = D) r = -0.14

2 5. Of points 1, 2, and 3 shown below, which is the most influential? That is, which would affect the linear regression line the most. A) 1 B) 2 C) 3 D) 1 and 3 are equally influential 6. We would expect the linear correlation coefficient between the two variables "age of a car" and "price of a car" to be A) positive B) negative C) zero D) very big For problems #7-14 you need to show work where possible and/or state which calculator program and parameters you are using for your calculations. Unless otherwise stated, round final answers to three decimal places. 8. A fair coin is tossed four times. (a) How many possible outcomes are there? (b) What is the probability of getting at least one head? 9. In a group of 15 people, 11 own a smartphone. Suppose 2 people are randomly selected from this group, without replacement. (a) Draw a tree diagram for this experiment, carefully labeling the tree with the outcomes and their probabilities. 4 pts

3 (b) Let x represent the number of people out of those 2 selected that own a smartphone. Use the tree diagram to complete the probability distribution table for x : 4 pts x Px ( ) Is this a binomial experiment? Explain why or why not. 10. In a particular lottery one can win $5,000 or $100. A lottery ticket cost $1 and the probability distribution for the net win (profit) is shown below. x P(x) 7 pts , (a) What is the probability of winning something when buying one lottery ticket? (b) What is the expected profit from participating in this lottery? Is it an expected win or loss? 11. A recent study (August 2014) showed that 60% of college students admit to being addicted to their cell phone. (a) If a random sample of 40 college students is selected, what is the probability that exactly half of them are being addicted to their cell phones?

4 (b) If a random sample of 40 college students is selected, what is the probability that more than 30 of them are being addicted to their cell phones? Find the expected number of college students found in a sample of 40 that are addicted to their cell phone. 12. Peter has five books: a novel, a biography, a dictionary, a statistics textbook, and a comic book. Peter s bookshelf only has room for three books. (a) In how many ways can Peter choose and arrange (order) three books? (b) What is the probability that the books on his shelf are statistics textbook, dictionary, and comic book, in that order? What is the probability that the statistics textbook, dictionary, and comic book are the three books chosen, in any order? 8. A 12-sided die can be made from a geometric solid called a dodecahedron. Assume that a fair dodecahedron is rolled. The sample space for one roll is (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. (a) Find the probability of rolling a 10 (b) Find the probability of rolling a two-digit number If the die was rolled 3 times, how big would the sample space be? That is, how many possible outcomes are there?

5 13. The following table gives the two-way classification of 500 students based on sex and whether or not they suffer from math anxiety. You can leave all answers below in fraction form. Suffer From Math Anxiety Sex Yes No Male Female (a) If you randomly select one student from these 500 students, find the probability that this selected student suffer from math anxiety. (b) If you randomly select one student from these 500 students, find the probability that this selected student does not suffer from math anxiety or that the student is female. If you randomly select one student from these 500 students, Find the probability that this selected student is a female and that she suffers from math anxiety. (d) If you randomly select one student from these 500 students, find the probability that this selected student suffers from math anxiety, given that he is a male. (e) Are the events "the student suffer from math anxiety" and "the student is a male" independent? Support your answer using probabilities. (f) Are the events "the student suffer from math anxiety" and "the student is a male" mutually

6 exclusive? 14. The following data comparing the size of sand granules with the slope on the beach. The scatter-plot for this data is linear. Let diameter of sand granules be the independent variable (x) and let gradient of beach slope be the dependent variable (y). (a) (b) Find the linear correlation coefficient and write it below. Round your answer to four decimal places. Would you consider this correlation coefficient to be weak or strong? 1 pts Diameter of sand granules (mm) Gradient of beach slope (degrees) Find the equation of the regression line. Round any numbers in your equation to four decimal places. (d) If two beaches have sand granules that differ by 0.2 mm, by how much would you expect their beach slopes to differ, on average? (e) Predict the gradient of the beach slope of a beach where the median diameter of sand granules is 0.28 mm. (f) Circle the letter next to the response that BEST completes the sentence. From above data set we can conclude that A) small sand granules cause beaches to have a small gradient slope B) beaches with small gradient slopes cause small sand granules diameter C) large sand granules are often found on beaches that have a small gradient slope D) small sand granules are often found on beaches that have a small gradient slope