Tutors Answer Your Questions about Probability-and-statistics (FREE)
Question 1183791: Two people A and B are to draw alternately one ball at a time from an urn containing 3 white and 2 black balls, drawn balls not being replaced. If A takes the first turn, what is the probability that A will be the first to draw white?
Click here to see answer by Theo(13342)   |
Question 1183791: Two people A and B are to draw alternately one ball at a time from an urn containing 3 white and 2 black balls, drawn balls not being replaced. If A takes the first turn, what is the probability that A will be the first to draw white?
Click here to see answer by ikleyn(52750)  |
Question 1183804: Please help. A calculus professor plans classes so carefully that the length of his classes is uniformly distributed between 100.0 min. and 105.0 min. Let x be the random variable representing the length of his randomly selected class. Find the probability the class is greater than 103 min.
Click here to see answer by ikleyn(52750) |
Question 1183805: A continuous random variable has a uniform distribution. Find the probability of the given event.
Suppose the reaction time x (in minutes) of a certain chemical process follows a uniform probability distribution with 5≤x≤15 . Find the probability that the given reaction time is greater than 8 min.
Click here to see answer by ikleyn(52750) |
Question 1183813: Suppose the reaction time x (in min.) of a certain chemical process follows a uniform probability distribution with 5≤x≤15 . Find the probability that the given reaction time is between 10 min. and 14 min.
Click here to see answer by ikleyn(52750) |
Question 1183831: Question 5
A sociologist found that in a random sample of 50 retired men, the average number of jobs they had during their lifetimes was 7.2. The population standard deviation is 2.1.
a. Find the best point estimate of the population mean.
b. At 80% confidence level, estimate the margin of error.
c. Find the 80% confidence interval of the mean number of jobs.
d. How large a sample would be required if you want to be 99% confidence within 0.05?
e. Estimate the sample mean if at 95% confidence level, the confidence intervals is 52.3 < 𝜇 < 55.7.
f. Find the error bound at 80% confidence level using the 80% confidence interval calculated.
Click here to see answer by Boreal(15235)  |
Question 1183823: Apply the Central Limit Theorem to solve the following problem.
Assume that cans of soda are filled so that the actual amounts have a mean μ=12 oz. and standard deviation σ=1.1 oz . Use this information to find the probability that a sample of 36 randomly selected cans will have a mean weight of at least 12.11 oz.
Click here to see answer by Boreal(15235) |
Question 1183845: A basketball player makes 80% of his free throws. We set him on the free throw line and told him to shoot free throws until he misses. Let the random variable X be the number of free throws taken by the player until he misses.
Assuming that his shots are independent, what is the probability of this player missing a free throw for the first time on the fifth attempt?
0.08192
0.0016
0.00128
0.4096
Click here to see answer by greenestamps(13195)  |
Question 1183830: QUESTIONS 4
It is recently found that eating eggs does not increase a person’s cholesterol. Five hundred people participated in a study that lasted for 2 years. The participants were randomly put on either not to eat egg or eat egg in moderation. Their cholesterol levels were checked at the beginning and at the end of the study. Overall, the groups’ levels were not significantly different. The research reminds us that eating eggs is healthy if done in moderation. Many of the previous studies relating eggs and high cholesterol came to improper conclusions. Using this information, answer these questions.
a. What prompted the study?
b. What is the population under study?
c. Was a sample collected?
d. What was the hypothesis?
e. Were data collected?
f. Were any statistical tests run? Explain.
g. What was the conclusion?
Click here to see answer by ikleyn(52750) |
Question 1183847: When Mr. Jones arrived at the grocery there were 8 cases of soda on the shelf. One case contained 11 cans of soda, and each of the others contained 6. If Mr.Jones bought all 8 cases, how many cans of soda did he purchase at this store?
A. 53
B.54
C. 57
D. 59
Click here to see answer by ikleyn(52750) |
Question 1183784: A ball is randomly drawn from either basket 1 or basket 2. Basket 1 has 3 white balls and 4 black balls. Basket 2 has 2 white and 3 black balls. The drawn ball is then randomly put into either basket 3 or basket 4. Basket 3 has 3 white and 3 black balls. Basket 4 has 2 white and 4 black balls. A ball is then randomly drawn from either basket 3 or basket 4.
a) What is the probability of drawing a white ball in the 2nd attempt?
b) What is the probability of drawing a black ball in the 2nd attempt?
c) If the 2nd ball drawn is white, what is the probability that it came from basket 4?
d) If the 2nd ball drawn is black, what is the probability that it came from basket 1?
e) Which ball draw event is the most likely to happen? The least likely to happen?
Click here to see answer by greenestamps(13195) |
Question 1183858: 4. A box contains 5 red balls, 3 white balls and 2 green balls. Two balls will be taken at random, without replacement, and the colors noted (in order).
(a) If the first ball is red, what is the (conditional) probability that the second ball is also red? (You don’t need a formula for this)
(b) Draw the tree diagram for this experiment - show the probabilities on the branches (as in the model).
(c) What is the probability of getting two red balls?
(d) What is the probability of getting exactly one red ball?
Click here to see answer by ikleyn(52750) |
Question 1183860: QUESTIONS 4
It is recently found that eating eggs does not increase a person’s cholesterol. Five hundred people participated in a study that lasted for 2 years. The participants were randomly put on either not to eat egg or eat egg in moderation. Their cholesterol levels were checked at the beginning and at the end of the study. Overall, the groups’ levels were not significantly different. The research reminds us that eating eggs is healthy if done in moderation. Many of the previous studies relating eggs and high cholesterol came to improper conclusions. Using this information, answer these questions.
a. What prompted the study?
b. What is the population under study?
c. Was a sample collected?
d. What was the hypothesis?
e. Were data collected?
f. Were any statistical tests run? Explain.
g. What was the conclusion?
N.B.: Please I do not "understand" this that is why I am posting it here, else why would I bother posting here? It is because I need "help".
If you feel you can direct me to a site or possibly provide me with a youtube tutorial link, that'll be helpful I would really appreciate it.
Click here to see answer by ikleyn(52750) |
Question 1183888: i really don’t get the solution for this one
find the mean, median and mode
95 78 82 79 84 88 74 90 87 75
80 69 84 91 90 82 73 93 70 87
77 85 75 90 84 83 91 78 86 87
78 81 85 79 84 83 91 78 86 72
90 83 76 67 87 91 84 82 87 94
75 78 80 74 60
Click here to see answer by ikleyn(52750) |
Question 1183861: Urn 1 contains 2 blue and 3 green balls. Urn 2 contains 4 blue and 3 green balls. A ball is randomly drawn from urn 1, without replacement,
and then placed inside urn 2. A ball is then drawn randomly from urn 2 and placed back in urn 1. If a ball is to be randomly drawn from urn 1,
what is the probability that the ball is blue?
Click here to see answer by robertb(5830)  |
Question 1183894: The mean weight of the adult Australian animal Swamp Wallaby the previous year was 15.4kg with a standard deviation of 2.5kg. This year a sample of 35 Swamp Wallaby were randomly selected and their given mean weight was 14.6kg. At 0.05 significant level can we state that the mean weight of Swamp Wallaby does not differ from the previous year? (Two - Tailed test)
Click here to see answer by robertb(5830) |
Question 1183829: Question 3
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 country revealed that the average number of Facebook friends was 350. At α = 0.05,
a. Why was the sample collected?
b. Calculate the significant level for this hypothesis test.
c. Find the critical value for this test at α = 0.05.
d. Calculate the test value.
e. Based on the test value and the critical value is there enough evidence to conclude that the mean number of friends is greater than 338?
f. Determine whether it is a one - tail or a two - tail test.
g. Find the maximum error E for estimating population mean.
Click here to see answer by robertb(5830) |
Question 1183890: Urn 1 contains 2 white, 3 blue, and 4 red balls. Urn 2 contains 3 white and 5 blue balls. A ball is randomly drawn from urn 1, without replacement,
and then placed inside urn 2. A ball is then drawn randomly from urn 2 and placed back in urn 1. If a ball is to be randomly drawn from urn 1,
what is the probability that the ball is red? Is there a change in the probability of red from before the experiment? How would you explain your answer?
Click here to see answer by robertb(5830) |
Question 1183927: I am stuck on how to solve this. Use the given margin of error, confidence level, and population standard deviation σ to find the minimum sample size required to estimate an unknown population mean μ.
1. Margin of error: 1 inch; confidence level: 90%; σ = 2.5 inches
2. Margin of error: 0.5 inches; confidence level: 90%; σ = 2.4 inches
Click here to see answer by Theo(13342) |
Question 1183828: Q2. A random sample of 15 registered nurses in a large hospital showed that they worked on average 44.2 hours per week. The standard deviation of the sample was 2.6 hours per week.
a. Is this a large sample or a small sample? Explain.
b. Find the total number of hours worked by the sample.
c. What is the product of the sample size and the degrees of freedom?
d. What is the margin of error at 90% confidence level?
e. What are the confidence intervals?
f. Calculate the error bound in this case.
Click here to see answer by Boreal(15235) |
Question 1183826: The mean weight of the adult Australian animal Swamp Wallaby the previous year was 15.4kg with a standard deviation of 2.5kg. This year a sample of 35 Swamp Wallaby were randomly selected and their given mean weight was 14.6kg. At 0.05 significant level can we state that the mean weight of Swamp Wallaby does not differ from the previous year? (Two - Tailed test)
Click here to see answer by Boreal(15235) |
Question 1183816: Assume that adults have IQ scores that are normally distributed with mean μ=120 and standard deviation of σ=20 . Let x represent the IQ of a randomly selected adult. Solve the following problem. Hint: x=μ+(z⋅σ); z=x−μσ .
Find the IQ score separating the top 86% from the others.
Click here to see answer by Theo(13342) |
Question 1183962: Please help me solve equation.
Calculate the test statistic: X2= Σ (O−E)2E . The observed frequencies from three categories are: 7, 9, 14. Assume that we want to use 0.10 significance level to test the claim that the three categories are equally likely.
Click here to see answer by robertb(5830) |
Question 1183963: How do I solve this equation? Calculate the test statistic: X2= Σ (O−E)2E . The observed frequencies from three categories are: 5, 11, 14. Assume that we want to use 0.10 significance level to test the claim that the three categories have proportions of 0.20, 0.30, 0.50 respectively.
Click here to see answer by robertb(5830) |
Question 1183992: Scores for a particular standardized test are normally distributed with a mean of 80 and a
standard deviation of 14. Find the probability that a randomly chosen score is
i. No greater than 70
ii. At least 95
iii. Between 70 and 95
iv. A student was told that her percentile score on this exam is 72%. Approximately
what is her raw score?
Click here to see answer by Boreal(15235) |
Question 1183992: Scores for a particular standardized test are normally distributed with a mean of 80 and a
standard deviation of 14. Find the probability that a randomly chosen score is
i. No greater than 70
ii. At least 95
iii. Between 70 and 95
iv. A student was told that her percentile score on this exam is 72%. Approximately
what is her raw score?
Click here to see answer by Edwin McCravy(20054)  |
Question 1183990: A medical doctor who wanted to study the heights of adult men and women took a random
sample of 150 adult men and 120 adult women and found the following summary results.
Mean Height of Adult Men was 170cm and Standard Deviation of Adult Men was 8cm;
Mean Height of Adult Women was 164cm and Standard Deviation of Adult Women was 6cm.
Find a 90% confidence interval for the difference of mean height of adult men and
women.
Click here to see answer by Boreal(15235) |
Question 1183991: A random sample of 20 young men was taken. One half of the group was given coffee
containing caffeine while the other half was given decaffeinated coffee as the placebo
control. The pulse rate was measured after the subjects have drunk their coffee. The results
were:
12 men were given placebo with a mean of 65 and variance of 31.11
8 men were given Caffein with a mean of 78 and variance of 28.67
Test the hypothesis that caffeine has no effect on the pulse rates of young men (use a 1%
level of significance).
Click here to see answer by Boreal(15235) |
Question 1183989: The personnel manager of a company feels that 60% of the employees will have enhanced
skill after attending the training programme if they are sponsored for an in-house training
programme. A sample of records of 49 employees of the company, who attended the
training programme on skill development, reveals that only 24 of them are having enhanced
skill after attending the training programme. Find the probability that the sample of
employees who attended the training programme have enhanced their skill.
Click here to see answer by Boreal(15235) |
Question 1183989: The personnel manager of a company feels that 60% of the employees will have enhanced
skill after attending the training programme if they are sponsored for an in-house training
programme. A sample of records of 49 employees of the company, who attended the
training programme on skill development, reveals that only 24 of them are having enhanced
skill after attending the training programme. Find the probability that the sample of
employees who attended the training programme have enhanced their skill.
Click here to see answer by ikleyn(52750) |
Question 1182108: What is the probability that a sample mean calculated from a sample of 100 individuals from the Florida subdivision will have an average age between 64 and 66 years of age. As in question #2, the mean age of the population is 65 years of age, and the standard deviation is 2 years. For this problem, be sure to use the z-calculation that is for sample means.
Click here to see answer by Theo(13342) |
Question 1184024: A package of 6 bulbs are tested where the probability of an individual bulb is defective is
0.05. (That is, 5% of all the bulbs manufactured are defective).
i. What is the probability that two bulbs will be defective?
ii. What is the probability that at least one bulb will be defective?
iii. What is the probability that more than one bulb will be defective, given that at
least one is defective?
iv. Find the expected value of this distribution.
4
v. Find the standard deviation of this distribution?
Click here to see answer by ikleyn(52750) |
Question 1184028: Select the correct answer.
Which statement is true?
A. A sample statistic can never be equal to the population parameter.
B. Point estimates are defined for both samples and populations.
C. To calculate a sample proportion, we need to know the population size.
D. To calculate a point estimate, we need to know the sample size.
Click here to see answer by MathLover1(20849)  |
Question 1184029: Quincy is opening a bank account. He needs to create a personal identification number (PIN) for the automated teller machine and a password for online access to his account.
1. Quincy’s PIN must be a 4-digit number.
(a) Quincy asks the bank representative if digits can be used more than once. The representative says, “Yes, allowing for repetition reduces the likelihood of someone guessing your password.” Explain why this is true and calculate the probability of someone guessing a PIN in one try under each scenario.
Click here to see answer by Solver92311(821)  |
Question 1184042: The operations manager of a motor vehicle accessories firm with branches in Limpopo and Durban
wants to establish whether their Limpopo branch is performing better than their Durban branch
in terms of the average size of orders received. Both branches have been operating for only one
year. A random sample of 31 orders from the Limpopo branch had an average value of R355.20
with a standard deviation equal to R151.50. Orders received by the Durban branch of the firm
were also randomly sampled. The average of the 35 orders sampled was R265.60 with a sample
standard deviation of R162.20. Can the operations manager conclude, at the 3% significance level,
that the Limpopo branch is performing better than the Durban branch?
Click here to see answer by ikleyn(52750) |
Question 1184039: Hello, this might be a long question, but I think it is quite easy to do and I haven done it already, but apparently I got my answer wrong (16), can someone please explain to me why the answer is 12?
Knowledge I have to know to solve this question:
the inclusion-exclusion principle for three sets and Venn Diagrams
Question:
A group of 82 senior students all study at least one of Biology, Chemistry and Physics. The number of students who study all three subjects is equal to the number who study Biology and Chemistry but not Physics. The number of students who study all three subjects is also equal to the number who study Chemistry and Physics but not Biology. Finally, there are twice as many students who study Biology and Physics but not Chemistry, as those who study all three subjects. If the numbers of students studying Biology, Physics and Chemistry are 41, 35, and 30 respectively, determine the number of students who study both Biology and Physics.
Click here to see answer by ikleyn(52750) |
Question 1184023: Suppose that the number of accidents occurring on a highway each day is a Poisson
random variable with parameter λ =3.1
i. Find the probability that 3 or more accidents occur today
ii. Find the probability that no accident occur today
Click here to see answer by robertb(5830) |
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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, 21286..21330, 21331..21375, 21376..21420, 21421..21465, 21466..21510, 21511..21555, 21556..21600, 21601..21645, 21646..21690, 21691..21735, 21736..21780, 21781..21825, 21826..21870, 21871..21915, 21916..21960, 21961..22005, 22006..22050, 22051..22095, 22096..22140, 22141..22185, 22186..22230, 22231..22275, 22276..22320, 22321..22365, 22366..22410, 22411..22455, 22456..22500, 22501..22545, 22546..22590, 22591..22635, 22636..22680, 22681..22725, 22726..22770, 22771..22815, 22816..22860, 22861..22905, 22906..22950, 22951..22995, 22996..23040, 23041..23085, 23086..23130, 23131..23175, 23176..23220, 23221..23265, 23266..23310, 23311..23355, 23356..23400, 23401..23445, 23446..23490, 23491..23535, 23536..23580, 23581..23625, 23626..23670, 23671..23715, 23716..23760, 23761..23805, 23806..23850, 23851..23895, 23896..23940, 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