# Answered: Probabilities

One common system for computing a grade point average (GPA) assigns 4 points to an A, 3 points to a B, 2 points to a C, 1 point to a D, and 0 points to an F. What is the GPA of a student who gets an A in a 3-credit course, a B in each of two 4-credit courses, a C in a 3-credit course, and a D in a 4-credit course? Solutions= 4*3+3*2*4+3*2+4*1=46 3+2*4+3+4=18 46/18=2.555 The mean grade point score is Answer =2.5555 =2.6(Round to the nearest tenth as needed.) A student's course grade is based on one midterm that counts as 20% of his final grade, one class project that counts as 20% of his final grade, a set of homework assignments that counts as 50% of his final grade, and a final exam that counts as 10% of his final grade. His midterm score is 64, his project score is 85, his homework score is 78, and his final exam score is 76. What is his overall final score? What letter grade did he earn (A, B, C, D, or F)? Assume that a mean of 90 or above is an A, a mean of at least 80 but less than 90 is a B, and so on. Solutions. Part 1 0.2*64+0.2*85+0.5*78+0.1*76=76.4 His overall final score is 76.4 (Type an integer or a decimal. Do not round.) Part 2 His letter grade is C. Methods used that summarize or describe characteristics of data are called _______ statistics. Part 1 Methods used that summarize or describe characteristics of data are called Descriptive statistics. . A value at the center or middle of a data set is a(n) _______. 1 A value at the center or middle of a data set is a(n) measure of center. Which of the following is NOT a measure of center? Question content area bottom Part 1 Choose the correct answer below. median mean census Your answer is correct. mode The measure of center that is the value that occurs with the greatest frequency is the mode. Identify the symbols used for each of the following: (a) sample standard deviation; (b) population standard deviation; (c) sample variance; (d) population variance. a. The symbol for sample standard deviation is s . b. The symbol for population standard deviation is sigma σ . c. The symbol for sample variance is squared s2 . d. The symbol for population variance is sigma squared σ2 . The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 259.4 and a standard deviation of 66.3. (All units are 1000 cells/μL.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 1 standard deviation of the mean, or between 193.1 and 325.7? b. What is the approximate percentage of women with platelet counts between 60.5 and 458.3? a. Approximately 68.68% of women in this group have platelet counts within 1 standard deviation of the mean, or between 193.1 and 325.7. (Type an integer or a decimal. Do not round.) Part 2 b. Approximately 99.7%of women in this group have platelet counts between 60.5 and 458.3. (Type an integer or a decimal. Do not round.) Which measure of variation is most sensitive to extreme values? Range. Median Range Your answer is correct. Mean For data sets having a distribution that is approximately bell-shaped, _______ states that about 68% of all data values fall within one standard deviation from the mean. For data sets having a distribution that is approximately bell-shaped, the Empirical Rule states that about 68% of all data values fall within one standard deviation from the mean. The square of the standard deviation is called the _______. variance. S A successful basketball player has a height of 6 feet 2 inches, or 188 cm. Based on statistics from a data set, his height converts to the z score of 1.95. How many standard deviations is his height above the mean? The player's height is 1.951.95 standard deviation(s) above the mean. (Round to two decimal places as needed.) If your score on your next statistics test is converted to a z score, which of these z scores would you prefer: −2.00, −1.00, 0, 1.00, 2.00? Why? Answer B A. The z score of 0 is most preferable because it corresponds to a test score equal to the mean. B. The z score of 2.00 is most preferable because it is 2.00 standard deviations above the mean and would correspond to the highest of the five different possible test scores. Your answer is correct. C. The z score of 1.00 is most preferable because it is 1.00 standard deviation above the mean and would correspond to an above average test score. D. The z score of −1.00 is most preferable because it is 1.00 standard deviation below the mean and would correspond to an above average test score. E. The z score of −2.00 is most preferable because it is 2.00 standard deviations below the mean and would correspond to the highest of the five different possible test scores. A data value is considered _______ if its z-score is less than −2 or greater than 2. significantly low or significantly high Fill in the blank. Whenever a data value is less than the mean, the corresponding z-score is negative. Fill in the blank. In modified boxplots, a data value is a(n) _______ if it is above Q3+(1.5)(IQR) or below Q1−(1.5)(IQR). In modified boxplots, a data value is a(n) outlier if it is above Q3+(1.5)(IQR) or below Q1−(1.5)(IQR). Which of the following is NOT a value in the 5-number summary? 1 Choose the correct answer below. Median Q1 Minimum Answer Mean If A denotes some event, what does A denote? If P(A)=0.006, what is the value of P(A)? A. Event A is always unusual. B. Event A denotes the complement of event A, meaning that A and A share some but not all outcomes. C. Events A and A share all outcomes. D. Event A denotes the complement of event A, meaning that A consists of all outcomes in which event A does not occur. Your answer is correct. Part 2 If P(A)=0.006, what is the value of P(A)? P(A)=0.994 of the 100 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability that a randomly selected item is defective? Question content area bottom Part 1 The probability is 0.04. (Type an integer or a decimal. Do not round.) You are certain to get a red card when selecting 27 cards from a shuffled deck. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive. The probability is 1. (Type an integer or a decimal.) On their first date, Kelly asks Mike to guess the date of her birth, not including the year. Complete parts a through c below. Part 1 a. What is the probability that Mike will guess correctly? (Ignore leap years.) 1/365(Type an integer or a simplified fraction.) Part 2 b. Would it be unlikely for him to guess correctly on his first try? A. No, it is not unlikely for Mike to guess correctly on his first try, as the probability of a correct guess is very high. B. No, it is not unlikely for Mike to guess correctly on his first try, as the probability of a correct guess is very low. C. It is impossible for Mike to not guess correctly on his first try, as the probability of a correct guess is 1. D. Yes, it is unlikely for Mike to guess correctly on his first try, as the probability of a correct guess is very high. E. It is impossible for Mike to guess correctly on his first try, as the probability of a correct guess is 0. F. Yes, it is unlikely for Mike to guess correctly on his first try, as the probability of a correct guess is very low. Answer F. Your answer is correct. Part 3 c. If you were Kelly, and Mike did guess correctly on his first try, would you believe his claim that he made a lucky guess, or would you be convinced that he already knew when you were born? Mike already knew, as the probability of a correct guess is very low. Fill in the blank. The _______ for a procedure consists of all possible simple events or all outcomes that cannot be broken down any further. Question content area bottom Part 1 The sample space for a procedure consists of all possible simple events or all outcomes that cannot be broken down any further. Which of the following is NOT a principle of probability? Question content area bottom Part 1 Choose the correct answer below. Answer B A. The probability of any event is between 0 and 1 inclusive. B. All events are equally likely in any probability procedure. Your answer is correct. C. The probability of an impossible event is 0. D. The probability of an event that is certain to occur is 1. Fill in the blank. When using the _______ always be careful to avoid double-counting outcomes. Part 1 When using the addition rule always be careful to avoid double-counting outcomes. Fill in the blank. Events that are _______ cannot occur at the same time. Part 1 Events that are disjoint cannot occur at the same time. Fill in the blank. P(A)+PA = 1 is one way to express the _______. Part 1 P(A)+PA = 1 is one way to express the rule of complementary events. Which word is associated with multiplication when computing probabilities? Part 1 Choose the correct answer below. Answer And Disjoint And Your answer is correct. Or Not Fill in the blank. Two events A and B are _______ if the occurrence of one does not affect the probability of the occurrence of the other. Two events A and B are independent if the occurrence of one does not affect the probability of the occurrence of the other. Fill in the blank. Part 1 Selections made with replacement are considered to be independent. In horse racing, a trifecta is a bet that the first three finishers in a race are selected, and they are selected in the correct order. Does a trifecta involve combinations or permutations? Explain. Part 1 Choose the correct answer below. A. Because the order of the first three finishers does make a difference, the trifecta involves combinations. B. Because the order of the first three finishers does not make a difference, the trifecta involves combinations. C. Because the order of the first three finishers does not make a difference, the trifecta involves permutations. D. Answer: Because the order of the first three finishers does make a difference, the trifecta involves permutations. A thief steals an ATM card and must randomly guess the correct four-digit pin code from a 7-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try? Question content area bottom Part 1 The number of possible codes is 2401 (Type an integer or fraction. Simplify your answer.) Part 2 The probability that the correct code is given on the first try is 1/2401(Type an integer or fraction. Simplify your answer.) A Social Security number consists of nine digits in a particular order, and repetition of digits is allowed. After seeing the last four digits printed on a receipt, if you randomly select the other digits, what is the probability of getting the correct Social Security number of the person who was given the receipt? Question content area bottom Part 1 The probability is 1/100000(Type an integer or a simplified fraction.) If radio station call letters must begin with either K or W and must include either two or three additional letters, how many different possibilities are there? Part 1 There are 36504different possibilities. (Simplify your answer.) Question content area top Part 1 Winning the jackpot in a particular lottery requires that you select the correct five numbers between 1 and 43 and, in a separate drawing, you must also select the correct single number between 1 and 32. Find the probability of winning the jackpot. Part 1 The probability of winning the jackpot is 1/30803136. (Type an integer or simplified fraction.) Fill in the blank. For a sequence of events in which the first event can occur n1 ways, the second event can occur n2 ways, the third event can occur n3 ways, and so on, the events together can occur a total of n1•n2•n3•... ways. This is called _______. Part 1 For a sequence of two events in which the first event can occur m ways and the second event can occur n ways, the events together can occur a total of (m)(n) ways. This is called the multiplication counting rule. Which of the following is NOT a requirement of the Permutations Rule, nPr=n!(n−r)!, for items that are all different? Part 1 Choose the correct answer below. A. Order is taken into account (rearrangements of the same items are considered to be different). B. There are n different items available. C. Exactly r of the n items are selected (without replacement). D. Answer. Order is not taken into account (rearrangements of the same items are considered to be the same) Which of the following is NOT a requirement of the Combinations Rule, nCr=n!r!(n−r)!, for items that are all different? Part 1 Choose the correct answer below. Answer B A. That r of the n items are selected (without replacement). B. That order is taken into account (consider rearrangements of the same items to be different sequences). Your answer is correct. C. That there be n different items available. D. That order is not taken into account (consider rearrangements of the same items to be the same). Fill in the blank. If the order of the items selected matters, then we have a _______. permutation problem. s

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