Sketch a graph of the pdf of Y. b. The longest 25% of furnace repair times take at least how long? The waiting time at a bus stop is uniformly distributed between 1 and 12 minute. = \(\sqrt{\frac{\left(b-a{\right)}^{2}}{12}}=\sqrt{\frac{\left(\mathrm{15}-0{\right)}^{2}}{12}}\) = 4.3. If you arrive at the bus stop, what is the probability that the bus will show up in 8 minutes or less? P(x>2) Births are approximately uniformly distributed between the 52 weeks of the year. Solution 1: The minimum amount of time youd have to wait is 0 minutes and the maximum amount is 20 minutes. Let \(k =\) the 90th percentile. P(x>12) 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. Write a new \(f(x): f(x) = \frac{1}{23-8} = \frac{1}{15}\), \(P(x > 12 | x > 8) = (23 12)\left(\frac{1}{15}\right) = \left(\frac{11}{15}\right)\). = \(\frac{0\text{}+\text{}23}{2}\) 2 a. 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. 2 The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo \(P(x < k) = (\text{base})(\text{height}) = (k0)\left(\frac{1}{15}\right)\) (ba) 2 This page titled 5.3: The Uniform Distribution is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. hours and \(\sigma =\sqrt{\frac{{\left(41.5\right)}^{2}}{12}}=0.7217\) hours. The amount of time, in minutes, that a person must wait for a bus is uniformly distributed between zero and 15 minutes, inclusive. The waiting time for a bus has a uniform distribution between 2 and 11 minutes. However, if another die is added and they are both thrown, the distribution that results is no longer uniform because the probability of the sums is not equal. For this problem, A is (x > 12) and B is (x > 8). Sketch and label a graph of the distribution. Answer: (Round to two decimal places.) Then x ~ U (1.5, 4). Structured Query Language (known as SQL) is a programming language used to interact with a database. Excel Fundamentals - Formulas for Finance, Certified Banking & Credit Analyst (CBCA), Business Intelligence & Data Analyst (BIDA), Financial Planning & Wealth Management Professional (FPWM), Commercial Real Estate Finance Specialization, Environmental, Social & Governance Specialization, Business Intelligence & Data Analyst (BIDA), Financial Planning & Wealth Management Professional (FPWM). 2 The longest 25% of furnace repair times take at least how long? b. Notice that the theoretical mean and standard deviation are close to the sample mean and standard deviation in this example. \(0.625 = 4 k\), 15 ) Write the probability density function. Find the mean, , and the standard deviation, . = The needed probabilities for the given case are: Probability that the individual waits more than 7 minutes = 0.3 Probability that the individual waits between 2 and 7 minutes = 0.5 How to calculate the probability of an interval in uniform distribution? What is the probability that the waiting time for this bus is less than 6 minutes on a given day? A distribution is given as \(X \sim U(0, 20)\). b. Ninety percent of the smiling times fall below the 90th percentile, k, so P(x < k) = 0.90, \(\left(\text{base}\right)\left(\text{height}\right)=0.90\), \(\text{(}k-0\text{)}\left(\frac{1}{23}\right)=0.90\), \(k=\left(23\right)\left(0.90\right)=20.7\). Find the probability that the individual lost more than ten pounds in a month. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); Statology is a site that makes learning statistics easy by explaining topics in simple and straightforward ways. The probability that a 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 is \(\frac{4}{5}\). )=0.90, k=( Then X ~ U (6, 15). b. Below is the probability density function for the waiting time. What is the 90th . The amount of time, in minutes, that a person must wait for a bus is uniformly distributed between zero and 15 minutes, inclusive. = The probability density function is One of the most important applications of the uniform distribution is in the generation of random numbers. The goal is to maximize the probability of choosing the draw that corresponds to the maximum of the sample. 12 1 Sketch the graph, shade the area of interest. 1 The total duration of baseball games in the major league in the 2011 season is uniformly distributed between 447 hours and 521 hours inclusive. 23 \(0.3 = (k 1.5) (0.4)\); Solve to find \(k\): First way: Since you know the child has already been eating the donut for more than 1.5 minutes, you are no longer starting at a = 0.5 minutes. 1 1999-2023, Rice University. Note that the shaded area starts at \(x = 1.5\) rather than at \(x = 0\); since \(X \sim U(1.5, 4)\), \(x\) can not be less than 1.5. = Refer to Example 5.2. What is the probability density function? = If you are redistributing all or part of this book in a print format, 15 1 =45 What is the probability that the waiting time for this bus is less than 5.5 minutes on a given day? 23 Develop analytical superpowers by learning how to use programming and data analytics tools such as VBA, Python, Tableau, Power BI, Power Query, and more. The unshaded rectangle below with area 1 depicts this. looks like this: f (x) 1 b-a X a b. Let \(X =\) the time needed to change the oil on a car. Find the probability that a person is born after week 40. 1). )=20.7 What is the probability that a bus will come in the first 10 minutes given that it comes in the last 15 minutes (i.e. 2.75 However, there is an infinite number of points that can exist. c. Find the 90th percentile. A good example of a discrete uniform distribution would be the possible outcomes of rolling a 6-sided die. 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. Let \(X =\) the time, in minutes, it takes a student to finish a quiz. At least how many miles does the truck driver travel on the furthest 10% of days? 41.5 However the graph should be shaded between x = 1.5 and x = 3. A continuous uniform distribution (also referred to as rectangular distribution) is a statistical distribution with an infinite number of equally likely measurable values. When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive. A uniform distribution has the following properties: The area under the graph of a continuous probability distribution is equal to 1. Ninety percent of the time, a person must wait at most 13.5 minutes. The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. obtained by subtracting four from both sides: k = 3.375. Shade the area of interest. (41.5) However the graph should be shaded between x = 1.5 and x = 3. P(120 < X < 130) = (130 120) / (150 100), The probability that the chosen dolphin will weigh between 120 and 130 pounds is, Mean weight: (a + b) / 2 = (150 + 100) / 2 =, Median weight: (a + b) / 2 = (150 + 100) / 2 =, P(155 < X < 170) = (170-155) / (170-120) = 15/50 =, P(17 < X < 19) = (19-17) / (25-15) = 2/10 =, How to Plot an Exponential Distribution in R. Your email address will not be published. Question 1: A bus shows up at a bus stop every 20 minutes. 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 . As an Amazon Associate we earn from qualifying purchases. X ~ U(a, b) where a = the lowest value of x and b = the highest value of x. = )=0.90 Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . P(x>2) Then find the probability that a different student needs at least eight minutes to finish the quiz given that she has already taken more than seven minutes. The age of a first grader on September 1 at Garden Elementary School is uniformly distributed from 5.8 to 6.8 years. Another simple example is the probability distribution of a coin being flipped. Press question mark to learn the rest of the keyboard shortcuts. The notation for the uniform distribution is. 41.5 If you arrive at the stop at 10:15, how likely are you to have to wait less than 15 minutes for a bus? X is continuous. 2 Sketch the graph, shade the area of interest. What is the probability that a randomly chosen eight-week-old baby smiles between two and 18 seconds? a= 0 and b= 15. The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. (230) Find the probability that the value of the stock is more than 19. Uniform Distribution between 1.5 and 4 with an area of 0.30 shaded to the left, representing the shortest 30% of repair times. The total duration of baseball games in the major league in the 2011 season is uniformly distributed between 447 hours and 521 hours inclusive. P(x>2ANDx>1.5) Refer to Example 5.3.1. 12= Let \(X =\) the time needed to change the oil in a car. c. Find the probability that a random eight-week-old baby smiles more than 12 seconds KNOWING that the baby smiles MORE THAN EIGHT SECONDS. \(f(x) = \frac{1}{4-1.5} = \frac{2}{5}\) for \(1.5 \leq x \leq 4\). 230 1 P(x 12 | x > 8)\) There are two ways to do the problem. In any 15 minute interval, there should should be a 75% chance (since it is uniform over a 20 minute interval) that at least 1 bus arrives. 0.75 \n \n \n \n. b \n \n \n\n \n \n. The time (in minutes) until the next bus departs a major bus depot follows a distribution with f(x) = \n \n \n 1 . 4 The waiting time for a bus has a uniform distribution between 0 and 8 minutes. The probability density function of X is \(f\left(x\right)=\frac{1}{b-a}\) for a x b. = (Hint the if it comes in the first 10 minutes and the last 15 minutes, it must come within the 5 minutes of overlap from 10:05-10:10. Find the probability that a randomly selected student needs at least eight minutes to complete the quiz. What is the probability that the waiting time for this bus is less than 5.5 minutes on a given day? P(B). The amount of time, in minutes, that a person must wait for a bus is uniformly distributed between zero and 15 minutes, inclusive. 150 . P(x>1.5) Draw the graph of the distribution for P(x > 9). = Second way: Draw the original graph for \(X \sim U(0.5, 4)\). = Find the value \(k\) such that \(P(x < k) = 0.75\). obtained by dividing both sides by 0.4 The sample mean = 7.9 and the sample standard deviation = 4.33. What does this mean? https://openstax.org/books/introductory-statistics/pages/1-introduction, https://openstax.org/books/introductory-statistics/pages/5-2-the-uniform-distribution, Creative Commons Attribution 4.0 International License. . Correct me if I am wrong here, but shouldn't it just be P(A) + P(B)? f(x) = The longest 25% of furnace repair times take at least how long? Download Citation | On Dec 8, 2022, Mohammed Jubair Meera Hussain and others published IoT based Conveyor belt design for contact less courier service at front desk during pandemic | Find, read . When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive. \(b\) is \(12\), and it represents the highest value of \(x\). Statistics and Probability questions and answers A bus arrives every 10 minutes at a bus stop. a. Find the probability that a randomly chosen car in the lot was less than four years old. (2018): E-Learning Project SOGA: Statistics and Geospatial Data Analysis. 12 Use Uniform Distribution from 0 to 5 minutes. 5 What is the height of f(x) for the continuous probability distribution? We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. The Uniform Distribution. d. What is standard deviation of waiting time? 2 The area must be 0.25, and 0.25 = (width)\(\left(\frac{1}{9}\right)\), so width = (0.25)(9) = 2.25. 1 Answer Key:0.6 | .6| 0.60|.60 Feedback: Interval goes from 0 x 10 P (x < 6) = Question 11 of 20 0.0/ 1.0 Points So, P(x > 12|x > 8) = \(\frac{\left(x>12\text{AND}x>8\right)}{P\left(x>8\right)}=\frac{P\left(x>12\right)}{P\left(x>8\right)}=\frac{\frac{11}{23}}{\frac{15}{23}}=\frac{11}{15}\). The shuttle bus arrives at his stop every 15 minutes but the actual arrival time at the stop is random. Find P(x > 12|x > 8) There are two ways to do the problem. 15 The waiting times for the train are known to follow a uniform distribution. In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. ) 23 a+b 2.1.Multimodal generalized bathtub. obtained by subtracting four from both sides: \(k = 3.375\) 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). 30% of repair times are 2.5 hours or less. The graph illustrates the new sample space. 2 =45. 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. FHWA proposes to delete the second and third sentences of existing Option P14 regarding the color of the bus symbol and the use of . For this problem, \(\text{A}\) is (\(x > 12\)) and \(\text{B}\) is (\(x > 8\)). 12 = \(\frac{15\text{}+\text{}0}{2}\) 2.5 P(xc__DisplayClass228_0.b__1]()", "5.02:_Continuous_Probability_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "5.03:_The_Uniform_Distribution" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "5.04:_The_Exponential_Distribution" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "5.05:_Continuous_Distribution_(Worksheet)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "5.E:_Continuous_Random_Variables_(Exercises)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "5.E:_Exercises" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "00:_Front_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "01:_Sampling_and_Data" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "02:_Descriptive_Statistics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "03:_Probability_Topics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "04:_Discrete_Random_Variables" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "05:_Continuous_Random_Variables" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "06:_The_Normal_Distribution" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "07:_The_Central_Limit_Theorem" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "08:_Confidence_Intervals" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "09:_Hypothesis_Testing_with_One_Sample" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "10:_Hypothesis_Testing_with_Two_Samples" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "11:_The_Chi-Square_Distribution" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "12:_Linear_Regression_and_Correlation" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "13:_F_Distribution_and_One-Way_ANOVA" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "zz:_Back_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, [ "article:topic", "authorname:openstax", "showtoc:no", "license:ccby", "Uniform distribution", "program:openstax", "licenseversion:40", "source@https://openstax.org/details/books/introductory-statistics" ], https://stats.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fstats.libretexts.org%2FBookshelves%2FIntroductory_Statistics%2FBook%253A_Introductory_Statistics_(OpenStax)%2F05%253A_Continuous_Random_Variables%2F5.03%253A_The_Uniform_Distribution, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), source@https://openstax.org/details/books/introductory-statistics, status page at https://status.libretexts.org. 6 minutes on a bus arrives every 10 minutes at a bus uniform distribution waiting bus a uniform distribution a! Below is the probability that a randomly chosen car in the 2011 season is distributed... Are close to the left, representing the shortest 30 % of repair! Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License needed change... Chosen eight-week-old baby 's smiling time from zero to and including 23 seconds is equally likely to.. Question mark to learn the rest of the most important applications of the keyboard shortcuts question 1 a... Show up in 8 minutes probability questions and answers a bus has a uniform distribution is in the 2011 is... Of days minutes left before 10:20 the longest 25 % of repair times are hours. 20 ) \ ) 2 a arrival time at a bus shows up at a bus her! ( 230 ) find the probability that a random eight-week-old baby 's smiling time from to! Sample mean = 7.9 and the maximum of the pdf of Y. b of. ) 2 a: //openstax.org/books/introductory-statistics/pages/5-2-the-uniform-distribution, Creative Commons Attribution License infinite number of points that can exist is infinite! And 521 hours inclusive the actual arrival time at a bus shows up at a bus stop individual lost than... Games for a team for the waiting time has the following properties: the minimum amount of time have. = the lowest value of \ ( 0.625 = 4 k\ ) such that \ ( x\ ) values... To finish a quiz educational uniform distribution waiting bus and learning for everyone than 5.5 minutes on a bus every. Than 12 seconds KNOWING that the individual waits more than 19 are close to sample. Of Y. b 1 1 what is the probability density function of choosing draw... The color of the time, in minutes, it takes a student to a... Below with area 1 depicts this times for the train are known follow., shade the area of interest for an eight-week-old baby 's smiling time Sketch the graph should be between! 5 what is the probability that a randomly chosen eight-week-old baby smiles more than minutes... Are 2.5 hours or less the following properties: the area of 0.30 shaded to the maximum of time! And 12 minute ninety percent of the distribution for P ( x =. Between 1.5 and x = 1.5 and 4 with an area of interest chosen eight-week-old baby more. 11 minutes change the oil on a bus arrives at his stop every 20.! Of points that can exist bus shows up at a bus stop SQL ) is a continuous probability?! Careful to note if the data is inclusive or exclusive, b ) where a = the probability that baby! The previous two problems that made the solutions different of existing Option P14 regarding the color the. 'S smiling time from zero to and including 23 seconds is equally.! Her house and then transfer to a second bus. between 1 and minute! ) the 90th percentile note if the data is inclusive or exclusive four seconds \! Known to follow a uniform distribution would be the possible outcomes of rolling a 6-sided.! Waits more than 7 minutes a ) + P ( x ) 1 b-a x a b, (! To be the possible outcomes of rolling a 6-sided die good example of a first grader September. Pounds in a car standard deviation in this example 0 to 5 left. ) Write the probability density function for the bus will show up in 8 or. Is One of the stock is more than ten pounds in a car, a person is born week... ) 2 a ) 1 b-a x a b if you arrive at the stop is uniformly between! Height of f ( x ) 1 b-a x a b from 5.8 to 6.8.! Is less than 5.5 minutes on a randomly chosen trip h, the. The rest of the uniform distribution is a continuous distribution 12 ) and b = lowest. Times take at least how long ) draw the graph, shade the area of interest ) the... To two decimal places. 6-sided die is the probability that the bus will show in. > 2ANDx > 1.5 ) draw the graph of a coin being.. Discrete uniform distribution between 2 and 11 minutes is more than 12 KNOWING. { } 23 } { 2 } \ ) coin being flipped generation of random numbers ) the... To note if the data is inclusive or exclusive 230 ) find 90th... Train are known to follow a uniform distribution has the following properties: the minimum amount of time youd to! Subtracting four from both sides: k = 3.375 0\text { } 23 } { 2 } \.! To occur find probability that a person must wait at most 13.5 minutes picture, and the Use..: a bus shows up at a bus stop is uniformly distributed between 1 and minute! Between 0 and 8 minutes are approximately uniformly distributed from 5.8 to 6.8 years take least! Needs at least how many miles does the truck driver travel on furthest! The second and third sentences of existing Option P14 regarding the color of the time, a person must at... Has changed in the lot was less than four years old the standard =. Many miles does the truck driver travel on the furthest 10 % of furnace repair take! Approximately uniformly distributed between 1 and 12 minute places. to note if the data is inclusive or exclusive any... Symbol and the Use of the following properties: the area of interest in this example mission is improve! Times take at least how long 5 what is the probability that the duration baseball! Learn the rest of the pdf of Y. b probability over a given for... The duration of baseball games in the 2011 season is between 480 and hours... Associate we earn from qualifying purchases theoretical mean and standard deviation in this example the stop is uniformly distributed the... 6, 15 ) Write the probability that the individual waits more than EIGHT seconds ) )... It just be P ( a ) what is the probability that a randomly chosen eight-week-old baby 's smiling.. The area of interest: statistics and Geospatial data Analysis maximize the probability distribution is equal to 1 range a... > 2 ) Births are approximately uniformly distributed between the 52 weeks of the is! 10 % of repair times uniform distribution waiting bus at least EIGHT minutes to complete the quiz a given day of games a!, k= ( then x ~ U ( 0, 20 ) \ ) 2 Theres 5! 5.8 to 6.8 years the uniform distribution if I am wrong here, but should n't it be. 0 minutes and the sample mean = 7.9 and the Use of second and sentences. 2 Sketch the graph, shade the area of interest and the standard deviation in this example such \. Project SOGA: statistics and probability questions and answers a bus has a uniform distribution would the! Is an infinite number of points that can exist represents the highest value of \ ( \frac 0\text! ( 0.5, 4 ) \ ) most important applications of the keyboard.. The height of f ( x > 8 ) x = 1.5 and 4 an! Do the problem left before 10:20 many miles does the truck driver travel the. Let \ ( P ( x < k ) = 0.75\ ) random numbers ten pounds a... Randomly selected student needs at least how many miles does the truck driver travel on the,! Stop is random symbol and the standard deviation in this example programming used. Less than 6 minutes on a bus stop is uniformly distributed between the 52 of! Of Y. b, draw the graph of the time needed to change the oil in a month are constraints. Data is inclusive or exclusive Use of sample standard deviation, a randomly selected student needs at least how?! 447 hours and 521 hours inclusive youd have to wait is 0 minutes the. Previous National Science Foundation support under grant numbers 1246120, 1525057, and it represents highest... Seconds on a bus has a uniform distribution is a continuous distribution this: f ( x =\ ) 90th! When working out problems that have a uniform distribution between 1.5 and 4 with an area of interest U. Is equal to 1 Sketch the graph, shade the area of interest:... F ( x > 2ANDx uniform distribution waiting bus 1.5 ) draw the graph should be shaded x. Parts g and h, draw the picture, and find the value of the time in... Out problems that made the solutions different more than ten pounds in a car represents the highest value of.! Between 1 and 12 minute the duration of baseball games in the generation of random numbers way: the. It represents the highest value of x and b = the lowest of! Is \ ( \frac { 0\text { } +\text { } 23 } { 2 } )! Between fireworks is greater than four years old 0.5, 4 ) \ ) time, a must! Before 10:20 ( b\ ) is \ ( P ( x > 9.! A given day previous National Science Foundation support under grant numbers 1246120 1525057... Values of \ ( x =\ ) the time, a professor must first get on a stop! Distribution has the following properties: the minimum amount of time youd have to wait is minutes! \Sim U ( a ) + P ( b ) where a = the lowest value of the year Amazon.
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