Tutors Answer Your Questions about Probability-and-statistics (FREE)
Question 261280: I am trying to understand The Central Limit Theorem and do not quite understand the meaning where it states "the distribution of the mean will be approximately normal." Why is it advantageous to know that a distribution is approximately normal in The Central Limit Theorem? Thank you for your knowledge and help.
Click here to see answer by drk(1908)  |
Question 261280: I am trying to understand The Central Limit Theorem and do not quite understand the meaning where it states "the distribution of the mean will be approximately normal." Why is it advantageous to know that a distribution is approximately normal in The Central Limit Theorem? Thank you for your knowledge and help.
Click here to see answer by stanbon(57361) |
Question 261263: from a box containing 6 black balls and 4 green balls, 3 balls are drawn in sucession, each ball being replaced in the box before the next draw is made. what is the probability that all 3 are the same color? each color is presented?
Click here to see answer by Theo(3464)  |
Question 261324: In a packet of seeds, each has a .84 chance of germinating. Harold will plant 2 seeds.
Determine the probability of the following
a. Both seeds germinate
b. Neither seed germinate
c. at least one seed germinated
Click here to see answer by stanbon(57361) |
Question 261321: A question on a history test requires that 6 events be arranged in proper chronological order.
a. If someone were to guess on the order, how many different arrangements of the events would there be?
b. If Susan were guessing, what is the probability that she would get the answer correct?
Click here to see answer by stanbon(57361) |
Question 261315: Sally places 12 pieces of paper in a basket. Eight are yellow and four are red. Find the probability of the following.
a. if one piece of paper is drawn and is replaced before the second piece of paper is drawn, what is the probability of both pieces of paper being red?
b. Refer to "a" If the first piece of paper is not replaced before the second is drawn, what is the probability that both pieces of paper are red?
Click here to see answer by Theo(3464) |
Question 261184: A standard deck of 52 playing cards consists of four different suits
and 13 cards of different ranks in each suit. Four cards will be drawn at
random without replacement from this deck. The probability that the
four cards will be all the same suit is k times the probability that they
will be all the same rank. What is the value of k?
Click here to see answer by stanbon(57361) |
Question 261168: A financial analyst estimates that the probability that the economy will experience a recession is 30%. She also believes that if there is a recession the probability that her mutual fund will increase in value is 20%. If no recession, the probability that the fund will increase is 75%. Find the probability that the mutual fund will increase in value.
I think that the solution is the union of two complementary/mutually exclusive events: increase if there is crisis + increase if there is no crisis. 0.3*0.2+0.7*0.75 but according to the book the probability is a bit higher than what I've received by this
Click here to see answer by stanbon(57361) |
Question 261348: Draw a tree diagram to represent this problem. Use G for "germinates" and N for "fails to germinate." Be sure to include the probability on each branch.
The student supplied the missing info.
In a packet of seeds, each seed has a .84 chance of germinating. Harold will plant 2 seeds.
Click here to see answer by richwmiller(9143)  |
Question 261442: Question:
Construct a scatter plot using excel for the given data. Determine whether there is a positive linear correlation, negative linear correlation, or no linear correlation. Complete the table and find the correlation coefficient r.
x 3 5 2 8 2 4 4 5 6 3
y 65 80 60 88 66 78 85 90 90 71
Answer: 10 (340)-(42)(773)/square root 10(208)-42*42 square root 10(60,875)-773*773=-290.6/square root 3.16 square root 1.12=-1.585
This is what I have come up with
For the type of correlation is: negative linear correlation
Click here to see answer by stanbon(57361) |
Question 261439: Question:
In an area of the Midwest, records were kept on the relationship between the rainfall (in inches) and the yield of wheat (bushels per acre).
Rain fall, x 10.5 8.8 13.4 12.5 18.8 10.3 7.0 15.6 16.0
Yield, y 50.5 46.2 58.8 59.0 82.4 49.2 31.9 76.0 78.8
Find the equation of the regression line for the given data. Round the line values to the nearest two decimal places.
Answer: 9(7187.77)-(112.9)(532.8)/square root 9 (1521.39)-112.92 square root 9 (33,836.58)-532.8*532.8=453.6/square root 9.46 square root 2.06 =0.962
Using the equation found in part a, predict the bushel yield when the rainfall is 11 inches
Answer: 11(7187.77)-(112.9)(532.8)/square root (1521.39-112.92*112.92 square root 11 (33,836.58-532.8*532.8=189.1/square root 1.28 square root 1.82=1.440
This is what I have come up with.
Click here to see answer by stanbon(57361) |
Question 261376: Please help!!!!!!!!!!!! can someone show me step by step please so I can understand. Thank you
A math test was given a sample of the scores yielded the following results
88, 34, 18, 20, 4, 68, 1, 10, 99, 35, 61, 92, 67, 62,69, 22
find the range, standard deviation, and variance for the sample scores.
Click here to see answer by stanbon(57361) |
Question 261514: Im stuck on this question. can you please help?
Researchers at the Mayo Clinic have studied the effect of sound levels on patient healing and have found a significant association (louder hospital ambient sound level is associated with slower postsurgical healing). Based on the Mayo Clinic’s experience, Ardmore Hospital installed a new vinyl
flooring that is supposed to reduce the mean sound level (decibels) in the hospital corridors. The sound level is measured at five randomly selected times in the main corridor.
New Flooring.. Old Flooring
42.. 48
41.. 51
40.. 44
37.. 48
44.. 52
a) What are the null and alternative hypotheses to test if the variance in sound levels
has changed?
b) Using α = 0.05, what is the critical value for the hypothesis test?
c) What is the test statistic for the hypothesis test? You may find it helpful to use
excel to calculate the two sample variances
d) Draw a conclusion for the hypothesis test. Make sure you state your conclusion
in the context of the problem.
e) What is the p-value for the hypothesis test
Thanks!
Click here to see answer by stanbon(57361) |
Question 261722: A bag contains exactly three red marbles. five yellow marbles and two blue marbles.if three marbles are to be drawn from the bag at the same time,what is the probability that all three will be the same color? express your answer as a common fraction
Click here to see answer by stanbon(57361) |
Question 261695: A company specialises in packing of washing powder for a national chain of supermarkets.The machine used to pack the washing powder is calibrated to pack a mean of 510g.However,the packing machine is 100% reliable and there is some variation in the mean.The variability as measured by the standrd deviation is 2.5g.It is also known that the weight packed by the machine follows a normal distribution.The supermarket chain has recently been complaining because they think that too many washing powder boxes are either underweight or overweight.
a)What is the percentage of the bags filled by the machine will weigh less that 507.5g?
b)What is the probability that a bag filled by the machine weighs less than 512g?
c)What percentage of the bags will weigh between 512 and 515g?
Click here to see answer by stanbon(57361) |
Question 261681: An unscrupulous manufacturerknows that in a box of a dozen light bulbs,which he intends selling to a customer.four are in fact not working.He watches nervously as the customer insists on removing three and testing them.What is the probability that only one of the three tested fails to work?
Click here to see answer by stanbon(57361) |
Question 261478: Please help?
2. The mean amount of time a (unnamed) computer server is down is 18.3 minutes with a standard deviation of 5.7 minutes.
a. Assuming we know nothing about the shape of the data set, at least what percentage of times will the server be down between 8.325 and 28.275 minutes?
b. Assuming we can verify that the data set is approximately normally distributed, what percentage of times will the server be down less than 24 minutes?
c. Assuming we can verify that the data set is approximately normally distributed, 68% of the server downtimes will be within what range? (5 points)
Click here to see answer by stanbon(57361) |
Question 261728: You receive 14 tv's. Two of the tv's are defective. If two tv's are randomly selected, compute the probability that both tv's work. What is the probability at least one does not work?
-The probability that both tv's work is -
-The probability that at least one does not work is -
Click here to see answer by stanbon(57361) |
Question 261166: Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of pounds lost.
More than 10 pounds?
Click here to see answer by stanbon(57361) |
Question 261165: An unscruplolous manufacturer knows that in a box of dozen light bulbs ,which he intends selling to a customer,four are in fact not working .He watches nervously as the customer insists on removing three and tsting them.What is the probability that only one of the three tested fails to work?
Click here to see answer by stanbon(57361) |
Question 261154: A company specialises in packing washing powder for a National Chain of Supermarkets.The machine used to pack the washing powder is calibrated to make a mean of 510g.However the machine is not 100% reliable and there is some variation in the mean.The variability as measured by standard deviation is2.5g.It is known that the weight packed by the machine follows a normal distribution .The supermarket chain has recently been complaining because they think that too many washing powder boxes are either underweight or overweight.
a)What percentage of the bags filled by the machine will weigh less than 507.5g?
b)What is the probability that a bag filled by the machine weighs less than 512g?
c)What percentage of the bags will weigh between 512 and 515g?
Click here to see answer by stanbon(57361) |
Question 261119: Suppose that in the US the number of type O blood and type A blood are approximately the same. The
number of people with type B is 1/10 of those with type A and twice the number with type AB, Find the probablity that a randomly selcted individual is of type AB
Click here to see answer by stanbon(57361) |
Question 261791: In a pack of seeds, each seed has a .84 chance of germinating. Harold will plant 2 seeds.
a. Draw a tree diagram to represent this problem. Use G for "germinates" and N for "fails to germinate." Be sure to include the probability of each branch.
Determine the probability of the following:
b. Both seeds germinate
c. Neither seed germinated
d. At least one seed germinated
Click here to see answer by stanbon(57361) |
Question 261826: I understand basic probability but am very confused when it comes to the below question. I don't even have a clue where to start to solve this question.
A multiple choice test has 20 questions with each having 4 possible answers with one correct. Assume a student randomly guesses the answer to every question.
a. What is the probability of getting exactly 11 correct answers?
20x4=80 1 right answer from 1 question=1/4
b. What is the probability of getting less than 9 correct answers?
Click here to see answer by stanbon(57361) |
Question 261826: I understand basic probability but am very confused when it comes to the below question. I don't even have a clue where to start to solve this question.
A multiple choice test has 20 questions with each having 4 possible answers with one correct. Assume a student randomly guesses the answer to every question.
a. What is the probability of getting exactly 11 correct answers?
20x4=80 1 right answer from 1 question=1/4
b. What is the probability of getting less than 9 correct answers?
Click here to see answer by solver91311(16897)  |
Question 261908: In my class we were taught to find the probability by dividing the number of favorable outcomes by the number of outcomes in the sample space. I can find the sample space but how do I find the number of favorable outcomes in a problem?
Click here to see answer by solver91311(16897) |
Question 261861: From what I can understand of probability distribution I can only depict one not being a probability distribution which I have indicated below. I'm not sure what this question is asking in entirity as to if we only have to label the distribution probabilities or if we have to solve them as well. Any help you could provide is appreciated.
Decide whether the distribution is a probability distribution. If it is not a probability distribution, identify the property that is not satisfied.
x P(x) continuous probability distribution
1 0.200
2 0.238
3 0.245
4 0.307
Click here to see answer by stanbon(57361) |
Question 262250: Find the 99% confidence interval for the variance and standard deviation of the weights of 25 one-gallon containers of motor oil if a sample of 14 containers has a variance of 3.2. The weights are given in ounces. Assume the variable is normally distributed.
Click here to see answer by stanbon(57361) |
Question 261920: mean relative increase in stock price was about .83%, with a standard deviation of .20%
According to Chebyshev's theorm at least 84% lies between what two numbers.
I understand the theorm is supposed to be 2.5 Standard deviations but I don't see how that number is reached using the Formula. I get cought on the Algebra when the numbers are simplified to the point of
1-(1/K^2) = 0.84
1/k^2 = .16
what is done to make this so,
Click here to see answer by stanbon(57361) |
Question 262363: There is a Mega millions where one chooses 5 numbers from 56 numbers AND then chooses 1 number from 52.
Calculate the odds If you bought 1 ticket
NOW
Calculate the odds If you bought 100 tickets and explain why you are choosing the numerator value you selected for the # favorable events.
Click here to see answer by solver91311(16897) |
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 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, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660, 15661..15705, 15706..15750, 15751..15795, 15796..15840, 15841..15885, 15886..15930, 15931..15975, 15976..16020, 16021..16065, 16066..16110, 16111..16155, 16156..16200, 16201..16245, 16246..16290, 16291..16335, 16336..16380, 16381..16425, 16426..16470, 16471..16515, 16516..16560, 16561..16605, 16606..16650, 16651..16695, 16696..16740, 16741..16785, 16786..16830, 16831..16875, 16876..16920, 16921..16965, 16966..17010, 17011..17055, 17056..17100, 17101..17145, 17146..17190, 17191..17235, 17236..17280, 17281..17325, 17326..17370, 17371..17415, 17416..17460, 17461..17505, 17506..17550, 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, 20746..20790, 20791..20835, 20836..20880, 20881..20925, 20926..20970, 20971..21015, 21016..21060, 21061..21105, 21106..21150, 21151..21195, 21196..21240, 21241..21285
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