Tutors Answer Your Questions about Probability-and-statistics (FREE)
Question 1200613: A consumer advocacy group is doing a large study on car rental practices. Among other things, the consumer group would like to estimate the mean monthly mileage,u, of cars rented in the U.S. over the past year. The consumer group plans to choose a random sample of monthly U.S. rental car mileages and then estimate u using the mean of the sample.
Using the value 750 miles per month as the standard deviation of monthly U.S. rental car mileages from the past year, what is the minimum sample size needed in order for the consumer group to be 95% confident that its estimate is within 150 miles per month of u?
Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).
Click here to see answer by Theo(13342)   |
Question 1200611: Suppose the scores of students on an exam are Normally distributed with a mean of 488 and a standard deviation of 67. Then approximately 99.7% of the exam scores lie between the numbers
and
such that the mean is halfway between these two integers.
Click here to see answer by Theo(13342) |
Question 1200619: There are n balls in a box, each marked with a unique number from 1 to n. k balls are selected randomly from the box, and then returned to the box. What is the probability that the numbers on the selected balls satisfy the condition X1 < X2 < ... < Xk? Consider the case where n=20 and k=5.
Click here to see answer by ikleyn(52752)  |
Question 1200636: In a lecture class of 100 students, 12 are left handed. If two students are chosen at random, what is the probability that:
a) Both are left-handed
b) Neither are left-handed
c) Extend your probability tree diagram to show the possible outcomes if three students are chosen.
Click here to see answer by ikleyn(52752) |
Question 1200408: Many people believe that the average number of Facebook friends is 338. The population standard deviation is 43.2. A random sample of 50 high school students in a particular district revealed that the average number of Facebook friends was 350. At alpha=0.05, is there sufficient evidence to conclude that the mean number of friends is greater than 338?
Click here to see answer by Theo(13342) |
Question 1200621: Really Big Medical Center (RBMC) is testing patients who have spent time in grassy areas this summer and fall for Lyme disease. Suppose that the probability of someone with exposure to tall grass having Lyme is .3 (or 30 percent). You sample of 15 patients. You expect that 95% of the time the number of patients with Lyme disease will be between
and
. (HINT: Rememer the Empirical Rule.) Where applicable, keep 4 decimal places on intermediate calculations. Round your answers to 2 decimal places and put the numbers in carefully with no leading or trailing spaces. You may use leading zeros if needed.
Click here to see answer by Theo(13342) |
Question 1200679: In a high school graduating class of 100 students, 54 studied mathematics, 69 studied history,
and 35 studied both mathematics and history. If one of these students is selected at random,
find the probability that:
(a) the student took mathematics or history;
(b) the student did not take either of these subjects;
(c) the student took history but not mathematics.
Click here to see answer by ikleyn(52752) |
Question 1200688: In how many ways can the U.S senate select a chairperson, a treasurer and a secretary of a committee if all the senators are eligible for selection and no two senators from the same state can be selected together?
Click here to see answer by ikleyn(52752) |
Question 1200658: A food snack manufacturer samples 7 bags of pretzels off the assembly line and weighs their contents. If the sample mean is 15.2 oz and the sample standard deviation is 0.70 oz, find the 95% confidence interval of the true mean.
Click here to see answer by Theo(13342) |
Question 1200691: 2. A certain casino claims that the commonly known phrase "The House Always Wins" does not apply to one of their games called “streak". In this game, players pay $2.00 for a chance to toss a coin until the outcome "tails" is observed for a maximum of four tosses (i.e., you can keep tossing until "tails” are observed). The casino pays the player $1.00 for each toss, so the longer your "streak” the better. Is the casino's argument right? (Hint: Argue for or against using the expected gain).
Click here to see answer by greenestamps(13195)  |
Question 1200691: 2. A certain casino claims that the commonly known phrase "The House Always Wins" does not apply to one of their games called “streak". In this game, players pay $2.00 for a chance to toss a coin until the outcome "tails" is observed for a maximum of four tosses (i.e., you can keep tossing until "tails” are observed). The casino pays the player $1.00 for each toss, so the longer your "streak” the better. Is the casino's argument right? (Hint: Argue for or against using the expected gain).
Click here to see answer by ikleyn(52752) |
Question 1200708: The scores of students on the logic test of an entrance examination are normally distributed with a mean of 500 and a standard deviation of 100. Find the following test score probabilities.
(a) What is the probability a student scores over 400?
(b) What is the probability a student scores over 650?
(c) What is the probability a student scores under 375?
Click here to see answer by ikleyn(52752) |
Question 1200728: A restaurant offers it's customers a choice of 3 side dishes with each meal. the side dishes can be chosen from a list of fifteen possibilities with duplication allowed. For instance a customer can order two sides of mashed potatoes and one side of string beans. show that there are 680 possible choices for the three side dishes.
Click here to see answer by math_tutor2020(3816) |
Question 1200733: A factory needs two raw materials. The probability of not having an adequate supply of material A is 0.05, whereas the probability of not having an adequate supply of material B is 0.03. A study determines that the probability of a shortage in both A and B is 0.01. a. Let E be the event "shortage of A" and F be the event "shortage of B". Construct a Venn diagram representing events E and F.
Are events E and F independent explain
What proportion of the time can the factory operate? Explain
Click here to see answer by ikleyn(52752) |
Question 1200731: 1. A factory needs two raw materials. The probability of not having an adequate supply of material A is 0.05, whereas the probability of not having an adequate supply of material B is 0.03. A study determines that the probability of a shortage in both A and B is 0.01. a. Let E be the event "shortage of A" and F be the event "shortage of B". Construct a Venn diagram representing events E and F.
Are events E and F independent explain
What proportion of the time can the factory operate? Explain
Click here to see answer by ikleyn(52752) |
Question 1200741: In an box, there are numbered balls 1, 2, ..., n. Two balls are randomly drawn without replacement. What is the probability that the sum of the numbers written on the balls will be greater than x? It is known that the number on the first ball is even. What is the probability that the sum of the numbers on the balls will be greater than x?
([n, x] = [8, 13])
Click here to see answer by ikleyn(52752) |
Question 1200747: Assume that a randomly selected subject is given a bone density test. Bone density test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find P7, the 7th percentile. This is the bone density score separating the bottom 7% from the top 93%. The bone density score corresponding to P7 is
Click here to see answer by ikleyn(52752) |
Question 1200744: P% of the country's population have symptoms of a certain disease. When tested, a person with symptoms is diagnosed with a probability of p1, while a person without symptoms tests positive with a probability of p2. What is the probability that a randomly tested person will have a positive test result? What is the probability that a person who tested positive actually has symptoms of the disease? ([P, p1, p2] = [14, 0.96, 0.15])
Click here to see answer by ikleyn(52752) |
Question 1200745: A court consists of 3 judges. Two of them, independently of each other, make correct decisions with a probability of p. The third judge agrees with the first two decisions when they match. In case of different opinions of the first two judges, the third judge decides on his own and makes a mistake with a probability of q. What is the probability that the court will not make a mistake if the verdict is decided by a majority vote? ([p, q] = [0.5, 0.43])
Click here to see answer by math_tutor2020(3816) |
Question 1200745: A court consists of 3 judges. Two of them, independently of each other, make correct decisions with a probability of p. The third judge agrees with the first two decisions when they match. In case of different opinions of the first two judges, the third judge decides on his own and makes a mistake with a probability of q. What is the probability that the court will not make a mistake if the verdict is decided by a majority vote? ([p, q] = [0.5, 0.43])
Click here to see answer by ikleyn(52752) |
Question 1200758: In a survey, 30 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $42.9 and a standard deviation of $8.3. Estimate how much a typical parent would spend on their child's birthday gift (use a 99% confidence level). Give your answers to 3 decimal places.
Click here to see answer by math_tutor2020(3816) |
Question 1200753: A study of the amount of time it takes a specialist to repair a mobile MRI shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 broken mobile MRIs are randomly selected, find
the probability that their mean repair time is less than 8.9 hours
Click here to see answer by Theo(13342) |
Question 1200764: Let X be the ratio of sales to profits of some company. Assume that X has distribution function F(x) = 0 if x<2, F(x) = (x^2-4)/5 if 2 < x < 3, F(x) = 1 if x>3. What is the probability that X is between 2.5 and 5?
Click here to see answer by ikleyn(52752) |
Question 1200770: Three judges with a majority vote have to make a decision. The judges decide independently of each other. Based on previous experience, it is known that the probabilities of each judge making the correct decision are p1, p2, p3. What is the probability that the final decision will be correct? If the final decision was correct, what is the probability that the first judge made the right decision? ([p1, p2, p3] = [0.83, 0.83, 0.87])
Click here to see answer by ikleyn(52752) |
Question 1200773: An harbor is being attacked by n enemy planes. The harbor defense system launches two missiles at each plane, each of which independently destroys the target with a probability of p. What is the probability that at least two enemy planes will be shot down? (p = 0.71, n = 3)
Click here to see answer by ikleyn(52752) |
Question 1200783: It is reported that 15% of people who come into contact with a person infected with strep throat contract the disease. How might we use the random-number table to estimate the probability that at least one child in a three-child family will catch the disease, given that each child has come into contact with an infected person?
Click here to see answer by ikleyn(52752) |
Question 1200736: 16% of all Americans live in poverty. If 47 Americans are randomly selected, find the probability that
a. Exactly 7 of them live in poverty. _______
b. At most 6 of them live in poverty. ________
c. At least 8 of them live in poverty. _________
d. Between 5 and 10 (including 5 and 10) of them live in poverty. ________
Click here to see answer by Boreal(15235)  |
Question 1200659: In a survey of 468 registered voters, 152 of them wished to see Mayor Waffleskate lose her next election. The Waffleskate campaign claims that no more than 32% of registered voters wish to see her defeated. Does the 95% confidence interval for the proportion support this claim? (Hint: you should first construct the 95% confidence interval for the proportion of registered voters who whish to see Waffleskate defeated.)
Click here to see answer by Boreal(15235) |
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7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 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17551..17595, 17596..17640, 17641..17685, 17686..17730, 17731..17775, 17776..17820, 17821..17865, 17866..17910, 17911..17955, 17956..18000, 18001..18045, 18046..18090, 18091..18135, 18136..18180, 18181..18225, 18226..18270, 18271..18315, 18316..18360, 18361..18405, 18406..18450, 18451..18495, 18496..18540, 18541..18585, 18586..18630, 18631..18675, 18676..18720, 18721..18765, 18766..18810, 18811..18855, 18856..18900, 18901..18945, 18946..18990, 18991..19035, 19036..19080, 19081..19125, 19126..19170, 19171..19215, 19216..19260, 19261..19305, 19306..19350, 19351..19395, 19396..19440, 19441..19485, 19486..19530, 19531..19575, 19576..19620, 19621..19665, 19666..19710, 19711..19755, 19756..19800, 19801..19845, 19846..19890, 19891..19935, 19936..19980, 19981..20025, 20026..20070, 20071..20115, 20116..20160, 20161..20205, 20206..20250, 20251..20295, 20296..20340, 20341..20385, 20386..20430, 20431..20475, 20476..20520, 20521..20565, 20566..20610, 20611..20655, 20656..20700, 20701..20745, 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30331..30375, 30376..30420, 30421..30465, 30466..30510, 30511..30555, 30556..30600, 30601..30645, 30646..30690, 30691..30735, 30736..30780, 30781..30825, 30826..30870, 30871..30915, 30916..30960, 30961..31005, 31006..31050, 31051..31095, 31096..31140, 31141..31185, 31186..31230, 31231..31275, 31276..31320, 31321..31365, 31366..31410, 31411..31455, 31456..31500, 31501..31545, 31546..31590, 31591..31635, 31636..31680, 31681..31725, 31726..31770, 31771..31815, 31816..31860, 31861..31905, 31906..31950, 31951..31995, 31996..32040, 32041..32085, 32086..32130, 32131..32175, 32176..32220, 32221..32265, 32266..32310, 32311..32355, 32356..32400, 32401..32445, 32446..32490, 32491..32535, 32536..32580, 32581..32625, 32626..32670, 32671..32715, 32716..32760, 32761..32805, 32806..32850, 32851..32895, 32896..32940, 32941..32985, 32986..33030, 33031..33075, 33076..33120, 33121..33165, 33166..33210, 33211..33255, 33256..33300, 33301..33345, 33346..33390, 33391..33435, 33436..33480, 33481..33525, 33526..33570, 33571..33615, 33616..33660, 33661..33705, 33706..33750, 33751..33795, 33796..33840, 33841..33885, 33886..33930, 33931..33975, 33976..34020, 34021..34065, 34066..34110, 34111..34155, 34156..34200, 34201..34245, 34246..34290, 34291..34335, 34336..34380, 34381..34425, 34426..34470, 34471..34515, 34516..34560, 34561..34605, 34606..34650, 34651..34695, 34696..34740, 34741..34785, 34786..34830, 34831..34875, 34876..34920, 34921..34965, 34966..35010, 35011..35055, 35056..35100, 35101..35145, 35146..35190, 35191..35235, 35236..35280, 35281..35325, 35326..35370, 35371..35415, 35416..35460, 35461..35505, 35506..35550, 35551..35595, 35596..35640, 35641..35685, 35686..35730, 35731..35775, 35776..35820, 35821..35865, 35866..35910, 35911..35955, 35956..36000, 36001..36045, 36046..36090, 36091..36135, 36136..36180, 36181..36225, 36226..36270, 36271..36315, 36316..36360, 36361..36405, 36406..36450, 36451..36495, 36496..36540, 36541..36585, 36586..36630, 36631..36675, 36676..36720, 36721..36765, 36766..36810, 36811..36855, 36856..36900, 36901..36945, 36946..36990, 36991..37035, 37036..37080, 37081..37125, 37126..37170, 37171..37215, 37216..37260, 37261..37305, 37306..37350, 37351..37395, 37396..37440, 37441..37485, 37486..37530, 37531..37575, 37576..37620, 37621..37665, 37666..37710, 37711..37755, 37756..37800, 37801..37845, 37846..37890, 37891..37935, 37936..37980, 37981..38025, 38026..38070, 38071..38115, 38116..38160, 38161..38205, 38206..38250, 38251..38295, 38296..38340, 38341..38385, 38386..38430, 38431..38475, 38476..38520, 38521..38565, 38566..38610, 38611..38655, 38656..38700, 38701..38745, 38746..38790, 38791..38835, 38836..38880, 38881..38925, 38926..38970, 38971..39015, 39016..39060, 39061..39105, 39106..39150, 39151..39195, 39196..39240, 39241..39285, 39286..39330, 39331..39375, 39376..39420, 39421..39465, 39466..39510, 39511..39555, 39556..39600, 39601..39645, 39646..39690, 39691..39735, 39736..39780, 39781..39825, 39826..39870, 39871..39915, 39916..39960, 39961..40005, 40006..40050, 40051..40095, 40096..40140, 40141..40185, 40186..40230, 40231..40275, 40276..40320, 40321..40365, 40366..40410, 40411..40455, 40456..40500, 40501..40545, 40546..40590, 40591..40635, 40636..40680, 40681..40725, 40726..40770, 40771..40815, 40816..40860, 40861..40905, 40906..40950, 40951..40995, 40996..41040, 41041..41085, 41086..41130, 41131..41175, 41176..41220, 41221..41265, 41266..41310, 41311..41355, 41356..41400, 41401..41445, 41446..41490, 41491..41535, 41536..41580, 41581..41625, 41626..41670, 41671..41715, 41716..41760, 41761..41805, 41806..41850, 41851..41895, 41896..41940, 41941..41985, 41986..42030, 42031..42075, 42076..42120, 42121..42165, 42166..42210, 42211..42255, 42256..42300, 42301..42345, 42346..42390, 42391..42435, 42436..42480, 42481..42525, 42526..42570, 42571..42615, 42616..42660, 42661..42705, 42706..42750, 42751..42795, 42796..42840, 42841..42885, 42886..42930, 42931..42975, 42976..43020, 43021..43065, 43066..43110, 43111..43155, 43156..43200, 43201..43245, 43246..43290, 43291..43335, 43336..43380, 43381..43425, 43426..43470, 43471..43515, 43516..43560, 43561..43605, 43606..43650, 43651..43695, 43696..43740, 43741..43785, 43786..43830, 43831..43875, 43876..43920, 43921..43965, 43966..44010, 44011..44055, 44056..44100, 44101..44145, 44146..44190, 44191..44235, 44236..44280, 44281..44325, 44326..44370, 44371..44415, 44416..44460, 44461..44505, 44506..44550, 44551..44595, 44596..44640, 44641..44685, 44686..44730, 44731..44775, 44776..44820, 44821..44865, 44866..44910, 44911..44955, 44956..45000, 45001..45045, 45046..45090, 45091..45135, 45136..45180, 45181..45225, 45226..45270, 45271..45315, 45316..45360, 45361..45405, 45406..45450, 45451..45495, 45496..45540, 45541..45585, 45586..45630, 45631..45675, 45676..45720, 45721..45765, 45766..45810, 45811..45855, 45856..45900, 45901..45945, 45946..45990, 45991..46035, 46036..46080, 46081..46125, 46126..46170, 46171..46215, 46216..46260, 46261..46305, 46306..46350, 46351..46395, 46396..46440, 46441..46485, 46486..46530, 46531..46575, 46576..46620, 46621..46665, 46666..46710, 46711..46755, 46756..46800, 46801..46845, 46846..46890, 46891..46935, 46936..46980, 46981..47025, 47026..47070, 47071..47115, 47116..47160, 47161..47205, 47206..47250, 47251..47295, 47296..47340, 47341..47385, 47386..47430, 47431..47475, 47476..47520, 47521..47565, 47566..47610, 47611..47655, 47656..47700, 47701..47745, 47746..47790, 47791..47835, 47836..47880, 47881..47925, 47926..47970, 47971..48015, 48016..48060, 48061..48105, 48106..48150, 48151..48195, 48196..48240, 48241..48285, 48286..48330, 48331..48375, 48376..48420, 48421..48465, 48466..48510, 48511..48555, 48556..48600, 48601..48645, 48646..48690, 48691..48735, 48736..48780, 48781..48825, 48826..48870, 48871..48915, 48916..48960, 48961..49005, 49006..49050, 49051..49095, 49096..49140, 49141..49185, 49186..49230, 49231..49275, 49276..49320, 49321..49365, 49366..49410, 49411..49455, 49456..49500, 49501..49545, 49546..49590, 49591..49635, 49636..49680, 49681..49725, 49726..49770, 49771..49815, 49816..49860, 49861..49905, 49906..49950, 49951..49995, 49996..50040, 50041..50085, 50086..50130, 50131..50175, 50176..50220, 50221..50265, 50266..50310, 50311..50355, 50356..50400, 50401..50445, 50446..50490, 50491..50535, 50536..50580, 50581..50625, 50626..50670, 50671..50715, 50716..50760, 50761..50805, 50806..50850, 50851..50895, 50896..50940, 50941..50985, 50986..51030, 51031..51075, 51076..51120, 51121..51165, 51166..51210, 51211..51255, 51256..51300, 51301..51345
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