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Quiz Practice # 4 BioEpi 540, Fall 2003 1. 50% of all American children ages 6 to 14 have read the first Harry Potter book. Of those, 40% have also read the second Harry Potter book, and of those who had read the first two books, 20% have also read the third one. 1A If we choose at random an American child aged 6 to 14, what is the probability that she has read the first three Harry Potter books? A) B) C) D) E) F) 0 0 0 0 0 Something else or not enough information 1B If we choose at random an American child aged 6 to 14, what is the probability that she has read the first two Harry Potter books but not the third one? A) B) C) D) E) F) 0 0 0 0 0 Something else or not enough information 1C If we choose at random 12 American children aged 6 to 14, what is the probability that exactly 4 of them have read the first Harry Potter book? A) B) C) D) E) F) 0 0 0 0 0 Something else or not enough information 1D If we choose at random 12 American children aged 6 to 14, what is the probability that between 5 and 9, both inclusive, have read the first Harry Potter book? A) B) C) D) E) F) 0 0 0 0 0 Something else or not enough information 1 10/23/2003 be540af03practicequiz4 2. Suppose your original dataset consists of 100 distinct numbers where the smallest value is 2000 and the largest is 3000. You create a new dataset just by changing 2000 to 20 and leaving all the other numbers unchanged. Which of the following statements is true? A) B) C) D) E) F) The means will be different in the two datasets but the variances will be the same The range will be the same in both datasets The means will be different, but the medians and minima (P0) will remain the same The mean and the median will be the same in both datasets The Inter-Quartile Range (IQR) will be the same in both datasets Something else or not enough information 3. Student S has been studying all day in her underground apartment. She would like to know if it is raining outside, but the only information that she has is provided by the fact that her next door neighbor went out with an umbrella in her hands and her knowledge that the forecast for today called for a 40% chance of rain. Assume that the neighbor has a nine in ten chance of going out carrying an umbrella if it is raining outside (there is a one in ten chance that she will forget). Assume also that the neighbor goes out carrying an umbrella even in one of every ten days when there is no rain. 3A Given the information available, what is the probability that it is raining outside ? A) B) C) D) E) F) 0 0 0 0 0 Something else or not enough information 3B What would that probability be if the neighbor had come out without an umbrella ? A) B) C) D) E) F) 0 0 0 0 0 Something else or not enough information 3C What would that probability be if student S hadn t seen her neighbor come out ? A) B) C) D) E) F) 0 0 0 0 0 Something else or not enough information be540af03practicequiz4 2 10/23/2003 4. There are two tests regularly used to diagnose prostate cancer: measuring the level of the protein PSA in the blood and the Gleason score, based on microscopic analyses of a biopsy sample. Two groups of 1000 men chosen at random from the population were administrated each of the tests and then their prostate cancer status was evaluated, with the following results: Disease = YES 92 8 Disease = NO 60 840 PSA test = YES PSA test = NO 1000 Gleason test=YES Gleason test=NO Disease = YES 80 20 Disease = NO 30 870 1000 4A What is the specificity of the PSA test? A) B) C) D) E) F) 0 0 0 0 0 Something else or not enough information 4B What is the specificity of the Gleason test? A) B) C) D) E) F) 0 0 0 0 0 Something else or not enough information 4C What is the sensitivity of the PSA test? A) B) C) D) E) F) 0 0 0 0 0 Something else or not enough information be540af03practicequiz4 3 10/23/2003 4D What is the sensitivity of the Gleason test? A) B) C) D) E) F) 0 0 0 0 0 Something else or not enough information 4E Based only on the previous results, what would be a better test to use? A) B) C) D) E) F) 0 0 0 0 0 Something else or not enough information 5. Let A and B be two events such that P(A)=0.6 and P(B)=0.6. Which of the following MUST be true? A) B) C) D) E) A and B are independent A and B are mutually exclusive A and B are not mutually exclusive P(A and B)=0.2 P(A or B) = 1.2 6. Let A and B be two events such that P(A)=0.6 and P(A|B)=0.6. Which of the following is TRUE? A) B) C) D) E) A and B are independent A and B are mutually exclusive P(A or B) = 0.36 P(A and B) = 0.36 P(A or B) = 1.2 be540af03practicequiz4 4 10/23/2003 7. We choose 367 people at random. What is the probability that at least two of them share the same birthday (month and day) ? (Note : Assume that all birthdays are equally likely and all years have 365 days). A) B) C) D) E) F) 0.03 0.11 0.24 0.57 0.97 1.0 8. We choose 5 people at random. What is the probability that at least two of them share the same birthday (month and day)? (Note: Assume that all birthdays are equally likely and all years have 365 days). A) B) C) D) E) F) 0.03 0.11 0.24 0.57 0.97 1.0 9. Let A and B be two such events that P(A)=0.5, P(A and B)=0.25. 9A Assume that P(B)=0.3. Which of the following MUST be true ? A) B) C) D) E) F) A and B are independent P(A or B) = 0.15 A and B are mutually exclusive A and B are not independent P(A or B) = 0.8 Something else or not enough information 9B Assume now that P(B)=0.5. Which of the following MUST be true ? A) B) C) D) E) F) A and B are independent A and B are mutually exclusive P(A or B) = 0.25 A and B are not independent P(A or B) = 1.0 Something else or not enough information be540af03practicequiz4 5 10/23/2003 10. Basketball player P is a hot-hand shooter. If she shoots just one ball from the 3-point line she has a one in two chance of making a basket. After missing a shot her chances of making the next one are still one in two. But if she made the previous shot then her chances move to two in three, and if she made the previous two shots then her chances go to three in four.. 10A If player P shoots three times in a row, what is the probability that she will make all three baskets? A) B) C) D) E) F) 0 0 0 0 0 Something else or not enough information 10B If player P shoots three times in a row, what is the probability that she will miss all three baskets? A) B) C) D) E) F) 0 0 0 0 0 Something else or not enough information 10C If player P shoots three times in a row, what is the probability that she will make exactly two baskets? A) B) C) D) E) F) 0 0 0 0 0 Something else or not enough information be540af03practicequiz4 6 10/23/2003 11. Professor P performed an experiment to test the hypothesis that the more social relationships a person has, the less susceptible he or she is to getting a cold. The experiment was as follows : a group of 400 healthy people were grouped according to their number of relationships (such as parent, friend, neighbor, etc). They were then exposed to a virus that causes cold. The results are summarized in the following table: Number of Relationships Three or fewer Four to Seven Eight or More 46 92 24 54 108 76 Cold No cold Total Total 400 11A If one of the 400 people is selected at random, what is the probability that the person doesn t have a cold ? A) B) C) D) E) F) 0 0 0 0 0 Something else or not enough information 11B If one of the 400 people is selected at random and she has eight or more relationships, what is the probability that she doesn t have a cold ? A) B) C) D) E) F) 0 0 0 0 0 Something else or not enough information 11C If one of the 400 people is selected at random and she has a cold, what is the probability that she has three or fewer relationships ? A) B) C) D) E) F) 0 0 0 0 0 Something else or not enough information be540af03practicequiz4 7 10/23/2003 12. A recent sociological study revealed that married men living in the US with above average heights are 30% more likely to be married to women with above average height than to women of below average height. The same study also reported that the average height of married men and women in the US as being 171 cm and 165 cm., respectively. The standard deviation in both cases is 4 cm. 12A What is the expected value of the average combined height (sum of the heights of both spouses) of married couples in the US ? A) B) C) D) E) F) 0 0 0 0 0 Something else or not enough information 12B What is the variance of the combined height (sum of the heights of both spouses) of married couples in the US ? A) B) C) D) E) F) 0 0 0 0 0 Something else or not enough information 13. For a certain population diastolic blood pressure has been evaluated to have a mean value of 75, a first quartile (Q1) of 65, a third quartile (Q3) of 90, and a minimum of 50. What can we say for sure about diastolic blood pressure in that population? A) B) C) D) E) F) 25% of the values are between 65 and 75 25% of the values are between 75 and 90 25% of the values are between 50 and 65 50% of the values are between 50 and 75 50% of the values are between 50 and 65 Something else or not enough information be540af03practicequiz4 8 10/23/2003 14. UMass has three libraries : Morrill Library, which has only one floor, the Physical Sciences Library, which has four floors, and the Main Library, which has 28 floors. We choose a book from the UMass libraries according to the following procedure : first we choose one of the three libraries at random, then we choose a floor at random in the chosen library, and finally we choose a book at random in the chosen floor. 14A What is the probability that the chosen book will belong to the top floor in the Main Library? A) B) C) D) E) F) 0.0119 0.0357 0.2943 0.3333 0.3657 Something else or not enough information 14B What is the probability that the chosen book will not come from the Main Library ? A) B) C) D) E) F) 0.1515 0.3333 0.5 0.6667 0.8485 Something else or not enough information 14C Given that we are informed that the chosen book didn t come from the Main Library, what is the probability that it came from the 2nd floor in the Physical Sciences Library ? A) B) C) D) E) F) 0.125 0.2 0.25 0.3333 0.5 Something else or not enough information be540af03practicequiz4 9 10/23/2003

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