Tutors Answer Your Questions about Probability-and-statistics (FREE)
Question 129029: Use a diagram to list the sample space showing the possible arrangements of heads and tails when four coins are tossed. Then use the sample space to find the probability that
a. all four coins come up heads
b. exactly two coins come up heads
c. exactly three coins come up tails
d. at most two coins come up heads
e. at least two coins come up heads
f. no more than three coins come up tails.
Click here to see answer by stanbon(57361)  |
Question 128741: The default rate on government-guaranteed student loans at a certaing public 4-year institution is 7% (a) If 1,000 student loans are made, what is the probability of fewer than 50 defaults? (b) More than 100? Show your work carefully.
Click here to see answer by stanbon(57361) |
Question 129093: In Dallas, some fire trucks were painted yellow(instead of red) to heighten their visibility. During a test period, the fleet of red fire trucks made 153,348 runs and had 20 accidents, while the fleet of yellow fire trucks made 13,035 runs and had 4 accidents. At a= .01, did the yellow fire trucks have asignificantly lower accident rate? a) State the hypothesis. b)state the deicision rule and sketch it. c)find the sample proportions and z test statistic. d)make a decision. e) find the p-value and interpret it. f) if statistically significant, do you think the difference is large enough to be important? If so, who and why? g) is the normality assumption fulfilled? Explain.
Click here to see answer by stanbon(57361) |
Question 129078: Does lovastatin(a cholesterol-lowering drug) reduce the risk of heart attack? In a Texas study, researchers gave lovastatin to 2,325 people and an inactive substitute to 2,081 people(average age 58). After 5 years, 57 of the lovastatin group had suffered a heart attack, compared with 97 for the inactive pill. a) state the appropriate hypothesis. b) obtain a test statistic and p-value. Interpret the results at a=.01. c) Is normality assured? d) Is the difference large enough to be important? e)What else would medical researchers need to know before prescribing this drug widely? (Data are from Science News 153 [May 30, 1998],p. 343.)
Click here to see answer by stanbon(57361) |
Question 129135: I am having some problems with this problem...
Biting an unpopped kernel of popcorn hurts! As an experiemnt, a self-confessed connoisseur of cheap popcorn carefully counted 773 kernels and put them in a popper. After popping, the unpopped kernels were counted. There are 86.
(a) Construct a 90 percent confidence interval for the proportion of all kernels that would not pop.
(b) Check the normality assumption.
(c) Try the Very Quick Rule. Does it work well here?Why or why not?
(d) Why might this sample not be typical?
Click here to see answer by stanbon(57361) |
Question 129018: Daily Double: The daily double at most racetracks consists of selecting the winning horse in both the first and second races. If the first race has seven entries and the second race has eight entries, how many daily double tickets must you purchase to guarantee a win?
Click here to see answer by stanbon(57361) |
Question 129017: Roll a Die: Roll a die 50 times and record the results. Determine the empirical probability of rolling:
(a) a 1
(b) a 6
(c) does the probability of rolling a 1 appear to be the same as the probability of rolling a 6? Explain.
Click here to see answer by stanbon(57361) |
Question 128978: Need help! Please.....
In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 1,143 were positive. (a) construct a 95 percent confidence interval for the population proportion of positive drug tests. (b) why is the normality assumption not a problem, despite the very small value of p?
Course is online through UOP, I do not have an ISBN number for text books because the assignments are posted online. Thank you
Click here to see answer by stanbon(57361) |
Question 128887: Biting an unpopped kernel of popcorn hurts! As an experiemnt, a self-confessed connoisseur of cheap popcorn carefully counted 773 kernels and put them in a popper. After popping, the unpopped kernels were counted. There are 86.
(a) Construct a 90 percent confidence interval for the proportion of all kernels that would not pop.
(b) Check the normality assumption.
(c) Try the Very Quick Rule. Does it work well here?Why or why not?
(d) Why might this sample not be typical?
Click here to see answer by stanbon(57361) |
Question 128753: The probability is 1 in 4,000,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 50,000 trips. (a) What is the probability of a fatal accident over a lifetime? Explain your reasoning carefully. Hint: Assume independent events. Why might the assumption of independence be violated? (b) Why might a driver be tempted not to use a seat belt "just on this trip"?
You helped with this one,but the instructor is stating the probability is so small that it's undeterined how many will attemp; to not where a seat belt. where in the question does he come up with that answer? I am not seeing it.
Click here to see answer by stanbon(57361) |
Question 128922: Manager of Muddlepool FC has a squad of 16 players including 2 goakeepelrs, 5 defenders, 5 midfeilders and 4 forwards. He plays a 4 4 2 formation. So must always have 1 goalkeeper, 4 defenders, 4 midfeilders, and 2 forward. All players can be chosen but they need to play a fair amount of games.
How many different teams coud be chosen?
In the squad are 4 brothers. 1 is a goalkeeper, 1 is a defender, 1 is a midfeilder and 1 is a forward. The brothers parents come only to a game with at least two of the brothers. The team thinks the parents will only watch half of the games but the brothers think it is more than half.
In a season of 36 games how much more than half of the games are they likely to watch?
How would it differ using a 4 3 3 formation?
Click here to see answer by stanbon(57361) |
Question 129233: Please Help, I'm so confused on how to even start. Thanks!
Homework question:
2 teams: Boston Celtics and Denver Nuggets
Home team has 60% chance of winning; away team has 40% chance of winning.
What is the probability the Celtics will win the Championship at 4:2 out of 6 games:
1.) Draw the probability tree of the problem to explain answer?
Click here to see answer by stanbon(57361) |
Question 128586: A bag contains eight batteries, all of which are the same size and are equally likely to be selected. Each battery is a different brand. If you select two batteries at random, use the counting principle to determine how many points will be inthe sample space if the batteries are selected with replacement
Thank you for your help
Click here to see answer by stanbon(57361) |
Question 129435: Suppose that it is known that 5% of the items produced by a particular machine are defective in some way, and that we will choose a random sample of exactly 20 parts made by this machine.
a.What is the expected number of defective items, out of the 20 we select?
b.What is the probability that exactly 1 of the 20 items is defective?
c. what is the probability that no more than 2 out of the 20 items selected are defective.
Click here to see answer by stanbon(57361) |
Question 129457: Suppose that you take all of the black cards out of a standard deck of 52 cards and thoroughly shuffle the remaining 26 red cards. From this deck of 26 red cards you will select 3 cards, one at a time, WITHOUT replacement, and record weather each card is picked is a face card (a jack, queen, or king), or not a face card.
a.) What is the probability that none of the 3 cards picked in this way is a face card?
b.) what is the probability that exactly one of the three cards picked is a face card?
Click here to see answer by Edwin McCravy(8909)  |
Question 129555: Two students, Katie and Carly, are playing a game that uses ten different numbered cards lying face down on a table. The faces of the cards are labeled with one of the numbers from 1 to 10(each card has a different number). If Katie and Carly each turn over a different card, what is the probability that the sum of the two cards is even?
Click here to see answer by stanbon(57361) |
Question 129473: Assume that a local bank knows from past experience that between 10am and 11am each day the mean arrival rate is 60 customers per hour. Determine the probability that exactly 2 customers will arrive in any given one-minute interval between 10am and 11am.
Click here to see answer by stanbon(57361) |
Question 129456: Suppose that you take all of the black cards out of a standard deck of 52 cards and thoroughly shuffle the remaining 26 red cards. From this deck of 26 red cards you will select 3 cards, one at a time, WITHOUT replacement, and record weather each card is picked is a face card (a jack, queen, or king), or not a face card.
a.) What is the probability that none of the 3 cards picked in this way is a face card?
b.) what is the probability that exactly one of the three cards picked is a face card?
Click here to see answer by stanbon(57361) |
Question 129354: my mom is trying to help me with this problem, but we are not good at it. Can you continue to help us please? Here we go.
One thousand raffle tickets are sold for a firs prize $300. A second prize of $150. And a third prize of $50.00 dollars.What is a fair price to pay foe a raffle ticket? if Mary brought a raffle ticket for $1.00 dollar. What can you conclude about the cost of entering this raffle?. my mom says that i must do it this way.
1000 times $300.00 followed by $150.00 and so on. i know this is not right. Can you help us please?
Click here to see answer by stanbon(57361) |
Question 129297: Michael is one of five contestants entered in three races to be run on a five-lane track. If in each race the runners are assigned to the lanes at random, what is the probability that Michael will be assigned to the inside lane at least once?
I know that the total number of possible outcomes is 5!, so I assume this to be the starting denominator.
Click here to see answer by stanbon(57361) |
Question 129432: Problem 1:
Harold Hacker recently read in a national golf magazine that the average weekend golfer carries a handicap of 15 strokes and the standard deviation is 4 strokes. Harold manages a local men’s church league and just tallied the end-of-season totals. The 64 players in Harold’s league finished the year with an average handicap of 14 strokes.
a. Set up the null and alternative hypotheses to test if the average handicap in Harold’s league is not the same as the national average reported in the magazine.
b. Test your hypothesis using = 0.02.
c. Find the p value.
d. Based on Harold’s end-of-season data, what can you conclude?
Problem 2:
The players on last year’s football team at State College were able to bench press a mean of 312 lb. Coach Juarez made it clear to the players during spring training that the team’s average best lift had to improve. A special weight-training program was launched, and all the players participated. In an effort to measure the team’s progress, the coach recorded the heaviest lifts of the starting offensive and defensive lineups at the start of this season. Results are as follows:
346 412 332 285 396 461 321 275
246 315 298 347 430 419 406 311
319 385 377 365 385 400
a. State the appropriate null and alternative hypotheses.
b. Calculate the test statistic.
HINT sample mean=356.43 lb
Sample standard deviation = 56.05 lb
c. At = 0.01, should Coach Juarez reject the null hypothesis?
d. Assuming the starting lineup is a representative sample, what conclusion can the coach draw?
Problem 3:
a) Johnson’s Service Center has devised three potential options available to preferred customers who redeem coupons and buy at least 10 gallons of fuel when they stop in. Option A is a flat 3 cents off each gallon. Option B is a combination of 2 cents off plus another $1 discount on the regular price of a $5 deluxe car wash. Option C is a $2 discount on the same $5 deluxe car wash but no reduction in the fuel purchase. The owner, Harold Johnson, ran each option on three different two-week trial periods and tracked daily sales receipts from those customers who redeemed their coupons. Results are shown in the table below:
Option A Option B Option C
$453
507
513
521
511
615
601
552
551
505
515
512
476
427 $492
514
536
511
528
678
611
653
596
516
534
543
498
437 $467
525
516
500
435
462
411
674
512
559
624
711
512
416
a) State the null hypothesis to test for equal population means.
b) Below are the results from EXCEL of ANOVA of the data at the 0.05 level of significance. Do the sample data indicate the at least one of the three population mean total returns is different from the others? Why? (Explain using “F” and “Fcrit” – a drawing is fine.)
Anova: Single Factor
SUMMARY
Groups Count Sum Average Variance
Column 1 14 7259 518.5 2555.962
Column 2 14 7647 546.2143 4340.335
Column 3 14 7324 523.1429 8389.209
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 6169 2 3084.5 0.605377 0.550917 3.2381
Within Groups 198711.6 39 5095.168
Total 204880.6 41
Click here to see answer by stanbon(57361) |
Question 129314: WOW! I am lost on how to do this. I have read the chapter and I have tried to get this. Please help!Thank you!!!
An expert witness in a case of alleged racial discrimination in a state university school of nursing introduced a regression of the determinants of Salary of each professor for each year during an 8-year period (n=423) with the following results, with dependent variable Year (year in which the salary was observed) and predictors YearHire (year when the individual was hired), Race (1 if individual is black, o otherwise), and Rank (1 if individual is an assistant professor, o otherwise).
Interpret the results.
Variable-------Coefficient---------t---------------------p
Intercept-------3,816,521-------negative29.4-----------.000
Year------------1,948------------29.8------------------.000
YearHire------negative826-------negative5.5------------.000
Race----------negative2,093-----negative4.3------------.000
Rank----------negative6,438-----negative22.3-----------.000
r2=.811--------------r2adj=.809-----------s=3,318
Click here to see answer by stanbon(57361) |
Question 129644: Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more
should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 10
or below. The firm examined 35 randomly chosen fax transmissions during the next year, yielding
a sample mean of 14.44 with a standard deviation of 4.45 pages. (a) At the .01 level of significance,
is the true mean greater than 10? (b) Use Excel to find the right-tail p-value.
Click here to see answer by stanbon(57361) |
Question 129664: Lewis earned 85 on his biology midterm and 81 on his history midterm. In the biology class the mean score was 79 with standard deviation 5. In the history class the mean score was 76 with standard deviation 3.
a) Convert each midterm score to a standard z score.
b) On which test did he do better compared to the rest of the class
Click here to see answer by stanbon(57361) |
Question 129662: Long-term history has shown that 65% of all elected offices in a rural county have been won by Republican candidates. This year there are 5 offices up for public election in the county Let r be the number of public offices won by Republicans.
a) Find P(r) for r=0,1,2,3,4, and 5
b) Make a histogram for the r probability distribution.
c) What is the expected number of Republicans who will win office in the coming election?
d) What is the standard deviation of r?
Click here to see answer by stanbon(57361) |
Question 129661: Richard has just been given a ten-question multiple choice test in his history class. Each question has five answers only one of which is correct. Since Richard has not attended class recently, he does not know any of the answers. Assume that Richard guesses randomly on all ten questions.
a) Find the probability that he will answer all 10 questions correctly.
b) Find the probability that he will answer 5 or more questions correctly.
c) Find the probability that he will answer none of the questions correctly.
d) Find the probability that he will answer at least 3 questions correctly
Click here to see answer by stanbon(57361) |
Question 129660: Identify each of the random variables as continuous or discrete.
a) Speed of an automobile
b) The number of doughnuts left in the pantry
c) The air temperature of a public park
d) The weight of a professional wrestler
e) The number of restaurant patrons
Click here to see answer by stanbon(57361) |
Question 129659: Laura is training for a week-long mountain cycling tour. She has 12 short hilly routes from which to choose mid-week rides.
a) How many ways can she choose 4 different rides from the list for the first week's training if order matters?
b) How many ways can she choose 4 different rides if order does not matter?
c) If she has chosen the first weeks rides, how many ways can she choose four more different rides for the second week? Assume that order does not matter
Click here to see answer by stanbon(57361) |
Question 129772: I have a worksheet that I am having problem with. Can you please help?!
A lake is 120 fathoms deep. Use the fact that there are 6 feet in a fathom to tell the depth of the lake in feet.
I have tried 6/1=120/x and came up with an answer of 20 feet. I also tried6/1=x/120 and came up with an answer of 720 feet. I'm now sure if either is right. Neither answer looks right. Can you please help.
Thank you
Alicia
Click here to see answer by josmiceli(9686)  |
Question 129775: one card is randomly selected from a shuffled standard deck of 52 cards and then a die is rolled. find the probility of obtaining
a. a red card and a 1
b. a red card or a 1
c. a picture card and a 1
d. a picture card or a 1
e. a red picture card and a 1
f. a red picture card or a 1
Click here to see answer by oscargut(891)  |
Question 129775: one card is randomly selected from a shuffled standard deck of 52 cards and then a die is rolled. find the probility of obtaining
a. a red card and a 1
b. a red card or a 1
c. a picture card and a 1
d. a picture card or a 1
e. a red picture card and a 1
f. a red picture card or a 1
Click here to see answer by stanbon(57361) |
Question 129787: thank you for your answers to question 129775 but I did a,b,and c on my own and did not come up with your answers so could you please take me step by step through the process, because I am missing something.
Click here to see answer by oscargut(891) |
Question 129780: Please,I really need some help with this problem:
The manufacturer of Winston Tire Company (WTC) claims its new tires last for an average 45k miles. An independent testing agency road-tested 135 tires to substantiate the claim made by WTC. The sample mean was 44k miles with a sample standard deviation of 4k miles. Using 1% significance, determine if there is a reason to reject the claim made by WTC and conclude that the tires last for less than 45k miles.
Lets do this in an interactive fashion.
First, answer the following questions:
- what is 'n'
- calculate the confidence intervals (using 44k miles as your mean) (1% significance means 99% confidence)
Thanks...
Click here to see answer by stanbon(57361) |
Question 129839: How tall are college hockey players? The average height has been 68.3 inches. A random sample of 14 hockey players gave a mean height of 69.1 inches. We may assume that x has a normal distribution with σ = 0.9 inch. Does this indicate that the population mean height is different from 68.3 inches? Use 5% level of significance.
a) State the null and the alternate hypothesis.
b) Identify the sampling distribution to be used: the standard normal distribution or the Student's t distribution. Find the critical value(s).
c) Compute the z or t value of the sample test statistic.
d) Find the P value or an interval containing the P value for the sample test statistic.
e) Based on your answers to a through d, decide whether or not to reject the null hypothesis at the given significance level. Explain your conclusion in the context of the problem.
Click here to see answer by stanbon(57361) |
Question 129837: Roger has read a report that the weights of adult mail Siberian tigers have a distribution which is approximately normal with mean μ = 390 lb and σ = 65 lb.
a) Find the probability that an individual male Siberian tiger will weigh more than 450 lb.
b Find the probability that a random sample of 4 male Siberian tigers will have a sample mean weight more than 450 lb.
Click here to see answer by stanbon(57361) |
Question 129836: Researchers at a pharmaceutical company have found that the effective time duration of a safe dosage of a pain relief drug is normally distributed with mean 2 hours and standard deviation 0.3 hour. For a patient selected at random:
a) What is the probability that the drug will be effective for 2 hours or less?
b) What is the probability that the drug will be effective for 1 hour or less?
c) What is the probability that the drug will be effective for 3 hours or more?
Click here to see answer by stanbon(57361) |
Question 129893: Please help me ASAP!! Thanks!
In a bumper test, three types of autos were deliberately crashed into a barrier at 5 mph, and the
resulting damage (in dollars) was estimated. Five test vehicles of each type were crashed, with
the results shown below. Research question: Are the mean crash damages the same for these three
vehicles?
Click here to see answer by stanbon(57361) |
Question 129892: I need your help ASAP, Thank you!!
A sample of 25 concession stand purchases at the October 22 matinee of Bride of Chucky showed
a mean purchase of $5.29 with a standard deviation of $3.02. For the October 26 evening showing
of the same movie, for a sample of 25 purchases the mean was $5.12 with a standard deviation of
$2.14. The means appear to be very close, but not the variances. At α = .05, is there a difference
in variances? Show all steps clearly, including an illustration of the decision rule.
Click here to see answer by stanbon(57361) |
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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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