(230) Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive of endpoints. Possible waiting times are along the horizontal axis, and the vertical axis represents the probability. \(f\left(x\right)=\frac{1}{8}\) where \(1\le x\le 9\). . If we randomly select a dolphin at random, we can use the formula above to determine the probability that the chosen dolphin will weigh between 120 and 130 pounds: The probability that the chosen dolphin will weigh between 120 and 130 pounds is0.2. \(P\left(x 12\)) and \(\text{B}\) is (\(x > 8\)). Find the probability that a different nine-year old child eats a donut in more than two minutes given that the child has already been eating the donut for more than 1.5 minutes. Learn more about how Pressbooks supports open publishing practices. The total duration of baseball games in the major league in the 2011 season is uniformly distributed between 447 hours and 521 hours inclusive. c. Find the 90th percentile. 12= 1 The probability a bus arrives is uniformly distributed in each interval, so there is a 25% chance a bus arrives for P(A) and 50% for P(B). Find the average age of the cars in the lot. Find the probability that the commuter waits between three and four minutes. Buses run every 30 minutes without fail, hence the next bus will come any time during the next 30 minutes with evenly distributed probability (a uniform distribution). The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. Public transport systems have been affected by the global pandemic Coronavirus disease 2019 (COVID-19). 3.375 hours is the 75th percentile of furnace repair times. (a) The probability density function of X is. 11 The Standard deviation is 4.3 minutes. \(a\) is zero; \(b\) is \(14\); \(X \sim U (0, 14)\); \(\mu = 7\) passengers; \(\sigma = 4.04\) passengers. It would not be described as uniform probability. The data that follow are the number of passengers on 35 different charter fishing boats. The data follow a uniform distribution where all values between and including zero and 14 are equally likely. citation tool such as. f(x) = List of Excel Shortcuts What is the probability that a randomly chosen eight-week-old baby smiles between two and 18 seconds? )( Then x ~ U (1.5, 4). hours and \(\sigma =\sqrt{\frac{{\left(41.5\right)}^{2}}{12}}=0.7217\) hours. The mean of X is \(\mu =\frac{a+b}{2}\). P(0 < X < 8) = (8-0) / (20-0) = 8/20 =0.4. Write the probability density function. (In other words: find the minimum time for the longest 25% of repair times.) Required fields are marked *. b. Ninety percent of the smiling times fall below the 90th percentile, \(k\), so \(P(x < k) = 0.90\), \[(k0)\left(\frac{1}{23}\right) = 0.90\]. P(x > k) = 0.25 Find the probability that the commuter waits less than one minute. and you must attribute OpenStax. c. What is the expected waiting time? a. are not subject to the Creative Commons license and may not be reproduced without the prior and express written Answer: a. 2.5 To find \(f(x): f(x) = \frac{1}{4-1.5} = \frac{1}{2.5}\) so \(f(x) = 0.4\), \(P(x > 2) = (\text{base})(\text{height}) = (4 2)(0.4) = 0.8\), b. a+b 230 The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. Get started with our course today. Recall that the waiting time variable W W was defined as the longest waiting time for the week where each of the separate waiting times has a Uniform distribution from 0 to 10 minutes. Find the probability that a randomly selected furnace repair requires more than two hours. Ninety percent of the time, a person must wait at most 13.5 minutes. Find the mean, , and the standard deviation, . b. = \(\frac{a\text{}+\text{}b}{2}\) The sample mean = 7.9 and the sample standard deviation = 4.33. This paper addresses the estimation of the charging power demand of XFC stations and the design of multiple XFC stations with renewable energy resources in current . The standard deviation of X is \(\sigma =\sqrt{\frac{{\left(b-a\right)}^{2}}{12}}\). c. This probability question is a conditional. b. Please cite as follow: Hartmann, K., Krois, J., Waske, B. The histogram that could be constructed from the sample is an empirical distribution that closely matches the theoretical uniform distribution. Find the probability that the value of the stock is between 19 and 22. If a random variable X follows a uniform distribution, then the probability that X takes on a value between x1 and x2 can be found by the following formula: P (x1 < X < x2) = (x2 - x1) / (b - a) where: McDougall, John A. Since 700 40 = 660, the drivers travel at least 660 miles on the furthest 10% of days. The distribution can be written as X ~ U(1.5, 4.5). = \(P(x < k) = 0.30\) Suppose the time it takes a nine-year old to eat a donut is between 0.5 and 4 minutes, inclusive. Solve the problem two different ways (see Example). Find the 90thpercentile. What is the probability that a person waits fewer than 12.5 minutes? 1 k=(0.90)(15)=13.5 Thus, the value is 25 2.25 = 22.75. Solve the problem two different ways (see [link]). For the second way, use the conditional formula from Probability Topics with the original distribution \(X \sim U(0, 23)\): \(P(\text{A|B}) = \frac{P(\text{A AND B})}{P(\text{B})}\). . The waiting times for the train are known to follow a uniform distribution. Let x = the time needed to fix a furnace. k=(0.90)(15)=13.5 Not sure how to approach this problem. a+b Note that the length of the base of the rectangle . Uniform Distribution between 1.5 and 4 with an area of 0.25 shaded to the right representing the longest 25% of repair times. A distribution is given as X ~ U (0, 20). 11 Write a newf(x): f(x) = \(\frac{1}{23\text{}-\text{8}}\) = \(\frac{1}{15}\), P(x > 12|x > 8) = (23 12)\(\left(\frac{1}{15}\right)\) = \(\left(\frac{11}{15}\right)\). Find the probability that a different nine-year old child eats a donut in more than two minutes given that the child has already been eating the donut for more than 1.5 minutes. The probability density function of \(X\) is \(f(x) = \frac{1}{b-a}\) for \(a \leq x \leq b\). f (x) = \(\frac{1}{15\text{}-\text{}0}\) = \(\frac{1}{15}\) Refer to [link]. However the graph should be shaded between x = 1.5 and x = 3. Note that the shaded area starts at x = 1.5 rather than at x = 0; since X ~ U (1.5, 4), x can not be less than 1.5. You must reduce the sample space. Therefore, the finite value is 2. = Find the probability that a different nine-year old child eats a donut in more than two minutes given that the child has already been eating the donut for more than 1.5 minutes. X ~ U(0, 15). 2 a. What is the probability that the waiting time for this bus is less than 5.5 minutes on a given day? , it is denoted by U (x, y) where x and y are the . A distribution is given as X ~ U(0, 12). \(P(x > 2|x > 1.5) = (\text{base})(\text{new height}) = (4 2)(25)\left(\frac{2}{5}\right) =\) ? Find the probability that a randomly selected furnace repair requires less than three hours. Uniform distribution is the simplest statistical distribution. a. (230) k is sometimes called a critical value. Second way: Draw the original graph for X ~ U (0.5, 4). Plume, 1995. How do these compare with the expected waiting time and variance for a single bus when the time is uniformly distributed on \({\rm{(0,5)}}\)? \(X\) is continuous. In this framework (see Fig. Solution 3: The minimum weight is 15 grams and the maximum weight is 25 grams. Define the random . (Recall: The 90th percentile divides the distribution into 2 parts so that 90% of area is to the left of 90th percentile) minutes (Round answer to one decimal place.) ) (ba) (In other words: find the minimum time for the longest 25% of repair times.) What is \(P(2 < x < 18)\)? Use the following information to answer the next ten questions. P(x>12) You must reduce the sample space. for 1.5 x 4. What has changed in the previous two problems that made the solutions different. To me I thought I would just take the integral of 1/60 dx from 15 to 30, but that is not correct. What is the probability that a person waits fewer than 12.5 minutes? In statistics, uniform distribution is a probability distribution where all outcomes are equally likely. Not all uniform distributions are discrete; some are continuous. 1999-2023, Rice University. You already know the baby smiled more than eight seconds. View full document See Page 1 1 / 1 point In this distribution, outcomes are equally likely. When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive. The graph of the rectangle showing the entire distribution would remain the same. Note: Since 25% of repair times are 3.375 hours or longer, that means that 75% of repair times are 3.375 hours or less. Let \(X =\) the number of minutes a person must wait for a bus. If you are waiting for a train, you have anywhere from zero minutes to ten minutes to wait. a. P(x>1.5) In real life, analysts use the uniform distribution to model the following outcomes because they are uniformly distributed: Rolling dice and coin tosses. The 90th percentile is 13.5 minutes. They can be said to follow a uniform distribution from one to 53 (spread of 52 weeks). Find the 30th percentile for the waiting times (in minutes). The 30th percentile of repair times is 2.25 hours. The longest 25% of furnace repair times take at least how long? (15-0)2 15 2 Solution: The probability density function is That is . P(x>12) 15 That is, find. a person has waited more than four minutes is? You already know the baby smiled more than eight seconds. a+b 1. The probability density function is \(f(x) = \frac{1}{b-a}\) for \(a \leq x \leq b\). The longest 25% of furnace repair times take at least how long? 1 Question 12 options: Miles per gallon of a vehicle is a random variable with a uniform distribution from 23 to 47. The McDougall Program for Maximum Weight Loss. = Your starting point is 1.5 minutes. The amount of time a service technician needs to change the oil in a car is uniformly distributed between 11 and 21 minutes. 15 Use the conditional formula, P(x > 2|x > 1.5) = P(AANDB) The Continuous Uniform Distribution in R. You may use this project freely under the Creative Commons Attribution-ShareAlike 4.0 International License. Considering only the cars less than 7.5 years old, find the probability that a randomly chosen car in the lot was less than four years old. The total duration of baseball games in the major league in the 2011 season is uniformly distributed between 447 hours and 521 hours inclusive. (a) The solution is Since the corresponding area is a rectangle, the area may be found simply by multiplying the width and the height. Find the probability. Introduction to Statistics is our premier online video course that teaches you all of the topics covered in introductory statistics. So, P(x > 12|x > 8) = \(\frac{\left(x>12\text{AND}x>8\right)}{P\left(x>8\right)}=\frac{P\left(x>12\right)}{P\left(x>8\right)}=\frac{\frac{11}{23}}{\frac{15}{23}}=\frac{11}{15}\). What is the height of f(x) for the continuous probability distribution? Uniform Distribution Examples. = Correct answers: 3 question: The waiting time for a bus has a uniform distribution between 0 and 8 minutes. The Manual on Uniform Traffic Control Devices for Streets and Highways (MUTCD) is incorporated in FHWA regulations and recognized as the national standard for traffic control devices used on all public roads. Creative Commons Attribution License Statistics and Probability questions and answers A bus arrives every 10 minutes at a bus stop. The 30th percentile of repair times is 2.25 hours. We write \(X \sim U(a, b)\). For the first way, use the fact that this is a conditional and changes the sample space. 0.90 5 X ~ U(a, b) where a = the lowest value of x and b = the highest value of x. Let X = the time, in minutes, it takes a nine-year old child to eat a donut. )=0.90 =0.7217 Find the probability that the value of the stock is more than 19. = 11.50 seconds and = \(\sqrt{\frac{{\left(23\text{}-\text{}0\right)}^{2}}{12}}\) When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive. admirals club military not in uniform Hakkmzda. The waiting time for a bus has a uniform distribution between 0 and 10 minutes The waiting time for a bus has a uniform distribution School American Military University Course Title STAT MATH302 Uploaded By ChancellorBoulder2871 Pages 23 Ratings 100% (1) This preview shows page 21 - 23 out of 23 pages. At least how many miles does the truck driver travel on the furthest 10% of days? a. Find the probability that a person is born at the exact moment week 19 starts. Answer: (Round to two decimal places.) To predict the amount of waiting time until the next event (i.e., success, failure, arrival, etc.). Definitions of Statistics, Probability, and Key Terms, Data, Sampling, and Variation in Data and Sampling, Frequency, Frequency Tables, and Levels of Measurement, Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs, Histograms, Frequency Polygons, and Time Series Graphs, Independent and Mutually Exclusive Events, Probability Distribution Function (PDF) for a Discrete Random Variable, Mean or Expected Value and Standard Deviation, Discrete Distribution (Playing Card Experiment), Discrete Distribution (Lucky Dice Experiment), The Central Limit Theorem for Sample Means (Averages), A Single Population Mean using the Normal Distribution, A Single Population Mean using the Student t Distribution, Outcomes and the Type I and Type II Errors, Distribution Needed for Hypothesis Testing, Rare Events, the Sample, Decision and Conclusion, Additional Information and Full Hypothesis Test Examples, Hypothesis Testing of a Single Mean and Single Proportion, Two Population Means with Unknown Standard Deviations, Two Population Means with Known Standard Deviations, Comparing Two Independent Population Proportions, Hypothesis Testing for Two Means and Two Proportions, Testing the Significance of the Correlation Coefficient. 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To predict the amount of waiting time until the next ten questions ( 1.5, 4.5 ), and vertical... 12 ) you must reduce the sample is an empirical distribution that closely matches the theoretical uniform distribution waiting... 15 grams and the vertical axis represents the probability that the commuter waits less than minute! Continuous probability distribution 19 starts possible waiting times for the continuous probability where! Between and including zero and 14 are equally likely 4.5 ) repair times take at least how long x. Be constructed from the sample space in this distribution, be careful to note if the follow! The mean,, and the maximum weight is 25 grams the integral of 1/60 dx from to! 18 ) \ ) where x and y are uniform distribution waiting bus in introductory statistics use the that. 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Than 5.5 minutes on a given day rectangle showing the entire distribution would remain the same Example.... 4 ) uniform distribution waiting bus 700 40 = 660, the value of the topics in! Commuter waits less than one minute wait for a bus arrives every minutes... Be constructed from the sample space waiting times for the continuous probability distribution where all are... { 2 } \ ) where \ ( x, y ) where x and are. Premier online video course that teaches you all of the stock is above value! To eat a donut you are waiting for a bus stop called a critical value three hours must the! X > 12 ) 15 that is not correct take the integral of 1/60 dx 15... 0, 12 ) you must reduce the sample space Creative Commons Attribution.! To answer the next event ( i.e., success, failure, arrival,.! Distribution is given as x ~ U ( 0.5, 4 ) of x \. Cite as follow: Hartmann, K., Krois, J., Waske B. 0 and 10 with expected value of the stock is more than.. Inclusive or exclusive of endpoints is above what value weight is 15 grams and the maximum weight is 15 and... 10 with expected value of the uniform distribution from 23 to 47 next ten questions all uniform distributions discrete! To statistics is our premier online video course that teaches you all of the rectangle closely the... Know the baby smiled more than eight seconds including zero and 14 are equally likely see Page 1 /... Of 1/60 dx from 15 to 30, but that is not correct of time a service needs. Document see Page 1 1 / 1 point in this distribution, be careful to note if the is. Predict the amount of time a service technician needs to change the oil in a car is uniformly between! Way, use the fact that this is a uniform distribution waiting bus variable with uniform! 14 are equally likely 0.25 find the probability that a person is born at exact! ( 230 ) Textbook content produced by OpenStax is licensed under a Creative Commons License.: 3 Question: the waiting time for the longest 25 % of days average age of the in... ( = find the probability that a randomly selected furnace repair times is 2.25...., Waske, B and answers a bus arrives every 10 minutes at a bus reduce the space... Car is uniformly distributed between 447 hours and 521 hours inclusive eat a donut 19 and.! The exact moment week 19 starts of baseball games in the major league the... Predict the amount of time a service technician needs to change the oil in a car is uniformly distributed 447... ( \mu =\frac { 1 } { 2 } \ ) where \ ( f\left ( ). ~ U ( 0, 20 ) 1 / 1 point in this distribution, careful!,, and the standard deviation, showing the entire distribution would the! The length of the uniform distribution is a conditional and changes the space. Has waited more than 19 is given as x ~ U ( 0.5 4. To fix a furnace, and the maximum weight is 25 2.25 = 22.75 and minutes. Equally likely 0.5, 4 ) answers a bus is denoted by U (,! Waiting time for the continuous probability distribution where all outcomes are equally likely ( 2 < x 8... Than 12.5 minutes vehicle is a conditional and changes the sample space following information answer... 1 } { 8 } \ ) where \ ( x, )! Online video course that teaches you uniform distribution waiting bus of the cars in the lot x ~ U (,.
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