week.5.quiz - Determine whether the events E and F are...

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Unformatted text preview: Determine whether the events E and F are independent or dependent. Justify your answer. {a} E: A person having a high GPA. F: The same person being highly organized. C) A. E and F are independent because being highly organized has no effect on the probability of a person having a high GPA. {g B. E and F are dependent because being highly organized can affect the probability of a person having a high GPA. C} C. E and F are independent because having a high GPA has no effect on the probability of a person being highly organized. C} [.‘r. E and F are dependent because having a high GPA has no effect on the probability of a person being highly organized. {b} E: A randomly selected person coloring her hair black. F: Another randomly selected person coloring her hair blond. C} A. E can affect the probability of F, even if the two people are randomly selected, so the events are dependent. C} B. E can affect the probability of F because the people were randomly selected, so the events are dependent. C} C. E cannot affect F because "person 1 coloring her hair black" could never occur, so the events are neither dependent nor independent. {it} D. E cannot affect F and vice versa because the people were randomly selected, so the events are independent. {c} E: The war in a major oil—exporting country. F: The price ofgasoline. C) A. The war in a major oil—exporting country could not affect the price of gasoline, so E and F are independent. C} B. The price ofgasoline could affect the war in a major oil—exporting country, so E and F are dependent. {£1 C. The war in a major oil—exporting country could affect the price ofgasoline, so E and F are dependent. A probability experiment consists of rolling a fair lfl—sided die. Find the probability of the event below. rolling a number divisible by 2 The probability is [1.500 . [Type an integer or decimal rounded to three decimal places as needed.} About 80% of babies born with acertain ailment recover fully. A hospital is caring for six babies born with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values ofn, p, and q, and list the possible values ofthe random variable x. Is the experiment a binomial experiment? (0 Yes What is a success in this experiment? 0 Babydoesn'trecover O This is not a binomial experiment. © Babyrecovers Specify the value of n. Select the correct choice below and hit in any answer boxes in your choice. @A. “B O B. This is not a binomial experiment. Specify the value of p. Select the correct choice below and fill in any answer boxes in your choice. @a. p=I O B. This is not a binomial experiment. Specify the value of q. Select the correct choice below and fill in any answer boxes in your choice. @A- q:' 0 B. This is not a binomial experiment. List the possible values efthe random variable x. {ii} x=fl, 1,2,..., E- D x='1, 2, 3,..., E- l D x=fl,’l,2,...,5 L} This is not a binomial experiment. Students in a class take a quiz with eight questions. The number x of questions answered correctly can be approximated by the following probability distribution. Complete parts {a} through [9}. x 0 l 2 3 t1 5 E T 8 g PEx} 0.02 0.02 0.05 0.05 0.09 0.22 0.31 0.15 0.0? {a} Use the probability distribution to find the mean ofthe probability distribution. p=l [Round to the nearest tenth as needed.) [bl Use the probability distribution to ‘ind the variance of the probability distribution. 02 =. {Round to the nearest tentl‘ as needed} [cl Use the probability distribution to ‘ind the standard deviation of the probability distribution. [Round to the nearest tenth as reeded.) {d} Use the probability distribution to ‘ind the expected value ofthe probability distribution. [Round to the nearest tenth as reeded.) [el Interpret the results. EO it. The expected number of questions answered correctly is 5.3 with a standard deviation of 0.02 questions. E© B. The expected number of questions answered correctly is 5.3 with a standard deviation of 1.8 questions. EO C. The expected number of questions answered correctly is 1.8 with a standard deviation of 5.3 questions. ODTheexl’emd”“mhelfiqmtmanswere‘lmrl‘ECHT's3EW'EhaStanda'ddemt'onflli30mm“ A company that makes cartons finds that the probability of producing a carton with a puncture is 0.07, the probability that acarton has a smashed corner is 0.07, and the probability that a carton has a puncture and has a smashed corner is 0.005. Answer parts [a] and [bl below. [a] Are the events "selecting a carton with a puncture" and "selecting a carton with a smashed corner" mutually exclusive? Explain. O A. Yes, acarton can have a puncture and a smashed corner. 0 B. Yes, acarton cannot have a puncture and a smashed corner. 0 C. No, acarton cannot have a puncture and a smashed corner. 6) D. No, acarton can have a puncture and a smashed corner. [b] lia quality inspector randomly selects acarton, find the probability that the carton has a puncture or has a smashed corner. The probability that a carton has a puncture or a smashed corner is m. [Type an integer or a decimal. Do not round.) The table below shows the number of male and female students enrolled in nursing at a particular university for a recent semester. {a} Find the probability that a randomly selected student is male, given that the student is a nursing major. {b} Find the probability that a randomly selected student is a nursing major, given that the student is male. Nursing Majors Non-nursing majors Tc-tal lg Males 82 1125 121 T Females T35 1888 2:123 Tcrtal 82? 2813 38-48 {a} Find the probability that a randomly selected student is male, given that the student is a nursing major. The probability is 8.111 . [Round to three decimal places as needed} {b} Find the probability that a randomly selected student is a nursing major, given that the student is male. The probability is 8.8?8. [Round to three decimal places as needed} Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n =123, p =8.8-r1 The mean, p, is -. [Round to the nearest tenth as needed} The variance, (:2, is -. [Round to the nearest tenth as needed.]: The standard deviation, cr, is -. [Round to the nearest tenth as needed.) Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. lfconvenient, use the appropriate probability table or technologyto find the probabilities. A newspaperfnds that the mean number of typographical errors per page is five. Find the probability that (a) exactly four typographical errors are found on a page, (b) at most four typographical errors are found on a page, and (c) more than four typographical errors are found on a page. (a) P[exact|y four typographical errors are found on a page)=- (Round to fourdecimal places as needed.) (b) P[at most four typographical errors are found on a page) = [Round to fourdecimal places as needed.) (c) P[more than four typographical errors are found on a page)= [Round to fourdecimal places as needed.) I Which ofthe events are unusual? Select all that apply. ED A. The event in part (a) is unusual. ED B. The event in part (b) is unusual. ED C. The event in part (c) is unusual. E D. None ofthe events are unusual. Determine whether the distribution is adiscrete probability distribution. x PX b l] [1.15 l l]. l 2 [1.25 Is the distribution adiscrete probability distribution? Why? Choose the correct answer below. I Q A. Yes, because the probabilities sum to) and are all between 0 and 1, Inclusive. EEO B. No, because some ofthe probabilities have values greaterthan 1 or less than I]. if) C. No. because the total probability is not eoual to l. ‘v _. --: _______ _._ ____. r """"I ._ .__ _1__ __ .. Fifty percent ofhouseholds say they would feel secure ifthey had 050,000 in sayings. You randomly selects households and ask them ifthey would feel secure ifthey had 050,000 in savings. Find the probability that the number that say they would feel secure is la) exactly hire, (b) more than five, and (c) at most hire. (a) Find the probability that the number that say they would feel secure is exactly be. P[5)=- [Round to three decimal places as needed.) (b) Find the probability that the number that say they would feel secure is more than five. P[x>5)=- [Round to three decimal places as needed.) (c) Find the probability that the number that say they would feel secure is at most hire. Poss):- [Round to three decimal places as needed.) Perform the indicated calculation. 934 1134 C. 9 4 i = 2 [Round to the nearest thousandth as needed.) Outside a home, there is a Hey keypad with letters A, B, C, D, E, F, G, H, and I that can be used to open the garage if the correct nine-letter code is entered. Each key may be used only once. How many codes are possible? The number of possible codes is 362000 Adecter gives a patient a 70% chance otsuniving bypass surgery alter a heart attack. lfthe patient survives the surgery, then the patient has amt: chance that the heart damage will heal. Find the probability that the patient survives the surgery and the heart damage heals. The probability is 0.11 [Type an integer er a decimal.) Determine whether the random variable is discrete or continuous. a. The number of textbook authors now sitting at a computer. b. The number of points scored during a basketball game. c. The distance a baseball travels in the air alter being hit. d. The number of light bulbs that burn out in the next week in a room with 14 bulbs. e. The time it takes for a light bulb to burn out. [In I-Cl LIIE IIHIIIIJEI UI LEALIJUU'“. flHLIIUI-Cl IIU'II CIILLIIIH EL fl. 'LIU'IIIIJHLEI Ul-CI'L-IELE UI LUIILIIIHUHJ! {Q all. The random variable is discrete. CI B. The random variable is continuous. b. Is the number of points scored during a basketball game discrete or continuous? {it} A. The random variable is discrete. O B. The random variable is continuous. c. Is the distance a baseball travels in the air alter being hit discrete or continuous? 35} A. The random variable is continuous. ' The random variable is discrete. d. Is the number of light bulbs that burn out in the next week in a room with 1-1 bulbs discrete or continuous? {3 all. The random variable is discrete. x {i} B. The random variable is continuous. e. Is the time it takes for a light bulb to burn out discrete or continuous? 0 all. The random variable is continuous. x {Ii} B. The random variable is discrete. Use technology to [a] construct and graph a probability distribution and [b] describe its shape. The number ofcomputers per household in a small town Computers 0 1 2 3 Q1 Households 301 284 98 15 (a) Construct the probability distribution by completing the table below. it PM i x- 1 2 0.140 3- [Round to three decimal places as needed.) I Choose the correct graph ofthe probability distribution. I Use the irequencydistribution, which shows the number ofAmerican voters [in millions) according to age, tofind the probability that al'oterchosen at random is in the 18 to 20 Egg Fguefl Er years old age range. 18 to 20 5.? 21 to 24 8.5 25 to 34 20.2 35 to 44 25.4 45 to 54 52.7 55 and over 28.8 The probability that a wter chosen at random is in the 18 to 20 years old age range is 0.040. lRound to three decimal places as neededl Use the lrequencydistribution to the right, which shows the number olrroters [in millions) according to age, to find the probability that arroter chosen at random is in the given age range. 51E ofvoters Fguegb 8st 18 to El] . not between 21 and 24 [rears old 2t to Ed ll].3 M M 45 to 64 50.3 55 and over 25.? The probabilityr is 0.927. [Round to three decimal places as needed.) A standard deck ofcards contains 52 cards. Crne card is selected from the deck. [a} Compute the probability of randomly selecting ajack or ace. [b] Compute the probability of randomly selecting ajack or ace or four. [c} Compute the probability of randomly selecting a ten or spade. 2 a. F'flack or ace]: =l [Type an integer or a simplified fraction]: 3 b. Pfiack or ace or four]: = — [Type an integer or a simplified fraction.]r ‘13 :1. c. P[ten or spade} =5 [Type an integer or a simplified fraction} ...
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