Tutors Answer Your Questions about Probability-and-statistics (FREE)
Question 1167219: A scholarship committee has $3000 to award this year and has 12 qualified candidates. Fran thinks that individual awards of $1500, $1000, and $500 would be appropriate, while Pat thinks that 3 awards of $1000 each would seem logical. Answer the following questions.
a) Count the number of possible outcomes for each plan.
b) Explain which plan would allow the scholarship committee to reach a consensus most quickly.
Click here to see answer by ikleyn(52788)   |
Question 1160922: A student walks to school everyday. If it is not raining, the probability that he/she is not late is four times the probability that he/she is late. If it is raining, the probability that he/she is late is twice the probability that she/he is not late. On a particular day, it is three times as likely not to rain than it rains. On one particular day the student is late. What is the probability that it was raining on that day?
Click here to see answer by ikleyn(52788) |
Question 1159882: 7 men and 3 women are ranked according to their scores on an exam. Assume that no two scores are alike, and that all 10! possible rankings are equally likely. Let X denote the highest ranking achieved by a man (so X=1 indicates that a man achieved the highest score on the exam). Find each of the following:
P(X=1)=
P(X=2)=
P(X=3)=
P(X=7)=
Click here to see answer by ikleyn(52788) |
Question 1160790: A mathematics professor gives an "extra-credit" (bonus marks) problem on a test. If it is done correctly,15 points are added to the test score, and if it is done partially correctly,5 points are added; otherwise 5 points are subtracted. Suppose a student's probability of getting the problem completely right is 1/4, and only partially correct is 1/2.
Find the student's mathematical expectation 𝐸 (expected value) for extra credit.
Click here to see answer by ikleyn(52788) |
Question 1207399: In a large population, about
45
%
of people prefer tea over coffee. A researcher takes a random sample of
13
people and surveys whether they prefer tea over coffee.
Use the binomial distribution to compute the probability that exactly
6
of the people in the sample prefer tea over coffee.
Identify the following information required to find the probability of people who prefer tea over coffee.
Provide your answer below:
n =
trials
x =
successes
p =
probability of those who prefer tea (as a decimal, not percent)
Click here to see answer by ikleyn(52788) |
Question 1160934: Heights of men on a baseball team have a bell-shaped distribution with a mean of 172 cm and a standard deviation of 6 cm. Using the empirical rule, what is the approximate percentage of the men between the following values?
a. 154 cm and 190 cm
b. 160 cm and 184 cm
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Question 1165550: A box contains 17 large marbles and 14 small marbles. Each marble is either green or white. 10 of the large marbles are green, and 4 of the small marbles are white. If a marble is randomly selected from the box, what is the probability that it is small or white? Express your answer as a fraction or a decimal number rounded to four decimal places.
Click here to see answer by ikleyn(52788) |
Question 1165633: The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 108 hours. A random sample of 81 light bulbs indicated a sample mean life of 400 hours. Complete parts (a) through (d) below.
Click here to see answer by ikleyn(52788) |
Question 1197206: Suppose that 10% of the fields in a given agricultural**a) Average Number of Infested Fields**
* **Binomial Distribution:** This situation fits the binomial distribution:
* **Fixed number of trials:** 100 fields (n = 100)
* Two possible outcomes: infested or not infested
* Probability of success (infestation) is constant: p = 0.10
* Trials are independent
* **Mean of Binomial Distribution:**
* The average number of infested fields (mean) is given by: μ = n * p
* μ = 100 * 0.10 = 10 fields
**b) 95% Confidence Interval**
* **Standard Deviation of Binomial Distribution:**
* σ = √(n * p * (1 - p))
* σ = √(100 * 0.10 * 0.90) = √9 = 3
* **95% Confidence Interval:**
* For a normal distribution, approximately 95% of the data falls within 2 standard deviations of the mean.
* Lower Limit: μ - 2σ = 10 - 2 * 3 = 4 fields
* Upper Limit: μ + 2σ = 10 + 2 * 3 = 16 fields
* **Therefore, we would expect to find the number of infested fields within the range of 4 to 16 fields with a probability of approximately 95%.**
**c) Finding 25 Infested Fields**
* **25 infested fields is significantly higher than the expected range (4-16 fields).**
* **Possible Explanation:**
* **Violation of the assumption of independence:**
* If the infestation in one field increases the likelihood of infestation in nearby fields (e.g., due to pest migration), the trials would not be independent, and the binomial distribution might not accurately model the situation.
* **Change in infestation rate:**
* The actual infestation rate in the agricultural area might have increased significantly since the initial estimate of 10%.
* **Sampling bias:**
* The 100 fields selected might not be a truly random sample and may be more likely to be infested than the overall population of fields.
**In conclusion:**
Finding 25 infested fields in the sample suggests that the observed number of infested fields is significantly higher than expected under the assumption of a binomial distribution with a 10% infestation rate. This discrepancy could indicate a violation of the independence assumption or a change in the underlying infestation rate. Further investigation would be necessary to determine the cause of this unexpected result.
area are infested with the sweet potato whitefly. 100 fields in this area are randomly selected and checked for whitefly. a) What is the average number of fields sampled that are infested with whitefly? b) Within what limits would you expect to find the number of infested fields, with robability approximately 95%? c) What might you conclude if you found that x = 25 fields were infested? Is it possible that one of the characteristics of a binomial experiment is not satisfied in this experiment? Explain.
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Question 1199410: 4.4.2 Suppose that over a period of several years the average number of deaths from a certain noncontagious disease has been 10. If the number of deaths from this disease follows the Poisson distribution, what is the probability that during the current year: a. Exactly seven people will die from the disease? b. Ten or more people will die from the disease?
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Question 1167383: Assume that when adult with smartphone are randomly selected 43% ,use them in meeting or classes. If 10 adults smart phone users are randomly selected ,find the probability that at least 7 of them use their smartphone in meeting or class
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Question 1167732: 12,500 | 17,700 | 22,300
14,800 | 19,400 | 24,800
15,200 | 20,200 | 27,600
15,300 | 21,200 | 28,200
15,900 | 22,100 | 35,200
If the average and standard deviation of their components are 20,860 and 6, 168 respectively, determine the corresponding for the (use chebyshev theorem)
a.) 2nd standard deviation at the left side of the mean
Click here to see answer by CPhill(1959)  |
Question 1167739: 3. A manufacturer of certain bearing presents the following data pertaining to the diameters of the bearing for 10 hourly samples of size 4:
Hour Coded sample values
1 1.7 2.2 1.9 1.2
2 0.8 1.5 2.1 0.9
3 1.0 1.4 1.0 1.3
4 0.4 -0.6 0.7 0.2
5 1.4 2.3 2.8 2.7
6 1.8 2.0 1.1 0.1
7 1.6 1.0 1.5 2.0
8 2.5 1.6 1.8 1.2
9 2.9 2.0 0.5 2.2
10 1.1 1.1 3.1 1.6
Use X and R chart to determine if the process is in statistical control.
Click here to see answer by CPhill(1959) |
Question 1167889: The Democrat and Chronicle reported that 25% of the flights arriving at the San Diego airport during the
first five months of 2001 were late (Democrat and Chronicle, July 23, 2001). Assume the population
proportion is p .25.
a. Show the sampling distribution of , the proportion of late flights in a sample of 1000 flights.
b. What is the probability that the sample proportion will be within .03 of the population proportion if a
sample of size 1000 is selected?
c. Answer part (b) for a sample of 500 flights.
Click here to see answer by CPhill(1959) |
Question 1167902: 1. From past records it is known that the average life of a battery used in a digital clock is 305 days. The lives of the batteries are normally distributed. The battery was recently modifies to last longer. Samples of 20 modified batteries were tested. It was discovered that the mean life was 311 days, ant the sample standard deviation was 12 days. At the 0.05 level of significance, did the modification increase the mean life of the battery?
a. State the null and alternate hypotheses.
b. Show the decision graphically.
c. Compute t, and reach a decision.
d. Briefly summary your findings.
Click here to see answer by CPhill(1959) |
Question 1167903: 2. A Corkill Machine is set ti fill a small bottle with 9.0 grams of medicine. It is claimed that the mean weight is less 9.0 grams. The hypothesis is to be tested at the 0.01 level. A sample revealed these weights (in grams): 9.2, 8.7, 8.9, 8.6, 8.8, 8.5, 8.7, and 9.0.
a. State the null and alternate hypotheses.
b. How many degrees of freedom are there?
c. Give the decision rule.
d. Compute t-value and arrive at a decision.
Click here to see answer by CPhill(1959) |
Question 1167904: 3. The net weight of a sample bottles filled by a machine manufactured by Edne, and the net weights of a sample filled by a similar machine manufactured by Orno, Inc., are:
Edne: 5, 8, 7, 6, 9, 7
Orno: 8, 10, 7, 11, 9, 12, 14, 9
At the 0.05 level o, is the mean weight of the bottles filled by the Orno Machine greater than the mean weight of the bottle filled by the Edne Machine?
Click here to see answer by CPhill(1959) |
Question 1167906: 4. In an effort to determine the most effective way to teach safety principles to a group of employees at university, four different methods were tried. Samples of 20 employees were randomly assigned to one of four groups. The first group was given programmed instruction booklets and worked through the course at their own face. The second group attended lectures. The third group watched television presentations, and the fourth was divided into small discussion groups. At the end of the sessions, a test was given to the four groups. A high of 10 points is the highest score. Test at the 0.05 level that there is no difference among the four means. The results are presented below:
Table 1. Test grades of employees.
Programmed Instruction Lecture TV Presentation Group Discussion
6 8 7 8
7 5 9 5
6 8 6 6
5 6 8 6
6 8 5 5
Click here to see answer by CPhill(1959) |
Question 1167907: 5. Prepare a sample computation and analysis of observation that involve test of significance using dependent (correlated) data. Examples are:
a. A Training Director wishes to find out whether or not a unique training program will increase employee efficiency (before and after the training).
b. Weights of pupil before and after the feeding program.
c. Giving incentives to sales person.
d. Intelligence scores after showing special movie.
Click here to see answer by CPhill(1959) |
Question 1167528: A survey found that women's heights are normally distributed with mean 63.4 in and standard deviation 2.5 in. A branch of the military requires women's heights to be between 58 in and 80 in.
a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or too tall?
b. If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new height requirements?
Click here to see answer by ikleyn(52788) |
Question 1167480: A survey found that women's heights are normally distributed with mean 63.4 in and standard deviation 2.2 in. A branch of the military requires women's heights to be between 58 in and 80 in.
a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or too tall?
b. If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new height requirements?
Click here to see answer by ikleyn(52788) |
Question 1167778: 2. A company is to hire two new employees. They have prepared a final list of eight candidates, all
of whom are equally qualified. Of these eight candidates, five are women. Suppose the
company decides to select two persons randomly from these eight candidates.
a. What is the probability that:
i. Both candidate selected are women?
ii. At least one candidate selected is a woman?
iii. Second candidate is a woman.
iv. First candidate is a woman given that the second candidate is a woman.
(2 + 3 + 4 + 2 = 11 marks)
b. Let X denote the number of women in this sample.
i. Write the probability distribution of X.
ii. Find the standard deviation of X
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Question 1165805: A small motor starts on the first attempt 3/8 of the time, on the second attempt 1/4 of the time, and on the third attempt 1/4 of the time.
Let the random variable X be the number of tries it takes to start the motor. So, for instance, P(X=1) is 3/8.
Use the definition of a probability mass function to find the probability it takes more than 3 tries to start the motor.
P(X > 3) ?
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Question 1167499: Suppose the probability of a server winning any given point in a tennis match is a constant p, with 0 ≤ p ≤ 1. Then the probability of the server winning a game when serving from deuce is given below.
f(p)=p^2/1-2p(1-p)
a. Evaluate f(0.79) and interpret the results.
f(0.79)= ** round to four decimal places as needed
When serving from deuce, the server will win approximately ___ out of 100 games. (round to the nearest integer as needed)
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Question 1160672: The times a teacher takes to grade one page of an exam are normally distributed with a mean of 4 minutes and a standard deviation of 1 minute. For about what percent of exams does a teacher grade one page in less than 7 minutes?
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Question 1167340: In 2004, the average American household received 92.6 channels. In 2008, the average American household received 118.6 channels. What is the annual rate of change from 2004 to 2008? What is a synonym for rate of change?
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Question 1166256: At the ministry of Health headquarters, you are in charge of rationing shangombo district the area affected by hunger.The following reports about daily calories value of food available per adult during current period arrive from your local investigators. The estimated requirement of an adult is taken at 3000 calories per day and the absolute minimum at 1250. Advise the ministry by commenting on the reported figures and determine which in your own opinion needs more urgent attention Area
mean standard deviation
X 2500 500
Y 2200 300
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Question 1165673: Five-digit codes are selected at random from the set {0, 1, 2, ..., 9} with replacement. If the random variable X denotes the number of zeros in randomly chosen codes, then what are the space and the probability density function of X?
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Question 1209733: 60% of all violent felons in the prison system are repeat offenders. If 45 violent felons are randomly selected, find the probability that
a. Exactly 26 of them are repeat offenders.
b. At most 29 of them are repeat offenders.
c. At least 29 of them are repeat offenders.
d. Between 25 and 33 (including 25 and 33) of them are repeat offenders.
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Question 1168408: 64% of all violent felons in the prison system are repeat offenders. If 48 violent felons are randomly selected, find the probability that
a. Exactly 28 of them are repeat offenders.
b. At most 30 of them are repeat offenders.
c. At least 32 of them are repeat offenders.
d. Between 28 and 34 (including 28 and 34) of them are repeat offenders.
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Question 1168409: 73% of all Americans live in cities with population greater than 100,000 people. If 35 Americans are randomly selected, find the probability that
a. Exactly 26 of them live in cities with population greater than 100,000 people.
b. At most 26 of them live in cities with population greater than 100,000 people.
c. At least 25 of them live in cities with population greater than 100,000 people.
d. Between 21 and 25 (including 21 and 25) of them live in cities with population greater than 100,000 people.
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Question 1209960: 55% of all shark attacks are not fatal. Let r be the number of nonfatal attacks out of a random sample of five shark attacks. a) What is the probability all five shark attacks are nonfatal? b) What is the probability that three or more of the five shark attacks are nonfatal? c) What is the expected number of nonfatal shark attacks out of the five? d) What is the standard deviation of the r-probability distribution?
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Question 1209959: A club buys tickets for 15 seats in a row for a local production and then sends the tickets randomly to the 15 people who ordered seats. Of these 15 people, 9 are actors and 6 are backstage workers. Find the probability that: a. An actor and backstage worker will receive tickets sitting together. b. The actors will be seated together, and the backstage workers will be seated together.
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Question 1176351: During a 52-week period, a company paid overtime wages for 18 weeks and hired temporary help for 9 weeks. During 5 weeks, the company paid overtime and hired temporary help. Let: O = overtime, T = temporary help.
a. What is the probability P(O OR T) ?
Round your answer to the nearest hundredth.
b. Are O and T independent?
c. Are O and T mutually exclusive?
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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, 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