uniform distribution waiting bus

$P(x < 4 | x < 7.5) =$ _______. 12 P(x 12 | x > 8) = (23 12)\left(\frac{1}{15}\right) = \left(\frac{11}{15}\right)\). Use the following information to answer the next eleven exercises. So, mean is (0+12)/2 = 6 minutes b. In statistics, uniform distribution is a term used to describe a form of probability distribution where every possible outcome has an equal likelihood of happening. This means that any smiling time from zero to and including 23 seconds is equally likely. 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. $0.75 = k 1.5$, obtained by dividing both sides by 0.4 Refer to [link]. c. Ninety percent of the time, the time a person must wait falls below what value? However, the extreme high charging power of EVs at XFC stations may severely impact distribution networks. . (41.5) However, there is an infinite number of points that can exist. As waiting passengers occupy more platform space than circulating passengers, evaluation of their distribution across the platform is important. Write the probability density function. 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. $X =$ a real number between $a$ and $b$ (in some instances, $X$ can take on the values $a$ and $b$). 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 unshaded rectangle below with area 1 depicts this. Thank you! 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 $\frac{4}{5}$. = for 0 x 15. If a person arrives at the bus stop at a random time, how long will he or she have to wait before the next bus arrives? 2 2 = 7.5. On the average, a person must wait 7.5 minutes. The interval of values for $x$ is ______. Write the distribution in proper notation, and calculate the theoretical mean and standard deviation. 5.2 The Uniform Distribution. You can do this two ways: Draw the graph where a is now 18 and b is still 25. obtained by dividing both sides by 0.4 For this problem, A is (x > 12) and B is (x > 8). P(x>2ANDx>1.5) The second question has a conditional probability. ( What is $P(2 < x < 18)$? 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. 12 The standard deviation of X is $\sigma =\sqrt{\frac{{\left(b-a\right)}^{2}}{12}}$. Find the probability that a randomly selected home has more than 3,000 square feet given that you already know the house has more than 2,000 square feet. P(B) Required fields are marked *. On the average, a person must wait 7.5 minutes. 30% of repair times are 2.25 hours or less. 2 Excel shortcuts[citation CFIs free Financial Modeling Guidelines is a thorough and complete resource covering model design, model building blocks, and common tips, tricks, and What are SQL Data Types? $b$ is $12$, and it represents the highest value of $x$. Suppose the time it takes a nine-year old to eat a donut is between 0.5 and 4 minutes, inclusive. 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. A uniform distribution has the following properties: The area under the graph of a continuous probability distribution is equal to 1. Find P(x > 12|x > 8) There are two ways to do the problem. In their calculations of the optimal strategy . Sketch and label a graph of the distribution. The data that follow record the total weight, to the nearest pound, of fish caught by passengers on 35 different charter fishing boats on one summer day. (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.) . On the average, how long must a person wait? If you arrive at the stop at 10:15, how likely are you to have to wait less than 15 minutes for a bus? Sketch the graph, shade the area of interest. Theres only 5 minutes left before 10:20. Your starting point is 1.5 minutes. Note that the length of the base of the rectangle . Sketch and label a graph of the distribution. for 8 < x < 23, P(x > 12|x > 8) = (23 12) (a) The probability density function of X is. Create an account to follow your favorite communities and start taking part in conversations. 1 15+0 You already know the baby smiled more than eight seconds. Refer to Example 5.3.1. 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. Let X = the time, in minutes, it takes a nine-year old child to eat a donut. a. For this reason, it is important as a reference distribution. a. c. Find the 90th percentile. Notice that the theoretical mean and standard deviation are close to the sample mean and standard deviation in this example. A bus arrives every 10 minutes at a bus stop. A subway train on the Red Line arrives every eight minutes during rush hour. $X$ = The age (in years) of cars in the staff parking lot. On the average, how long must a person wait? When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive of endpoints. The longest 25% of furnace repairs take at least 3.375 hours (3.375 hours or longer). b. The probability of drawing any card from a deck of cards. Write the distribution in proper notation, and calculate the theoretical mean and standard deviation. If we get to the bus stop at a random time, the chances of catching a very large waiting gap will be relatively small. The mean of $X$ is $\mu = \frac{a+b}{2}$. The lower value of interest is 17 grams and the upper value of interest is 19 grams. The amount of time a service technician needs to change the oil in a car is uniformly distributed between 11 and 21 minutes. e. $\mu = \frac{a+b}{2}$ and $\sigma = \sqrt{\frac{(b-a)^{2}}{12}}$, $\mu = \frac{1.5+4}{2} = 2.75$ hours and $\sigma = \sqrt{\frac{(4-1.5)^{2}}{12}} = 0.7217$ hours. Question 2: The length of an NBA game is uniformly distributed between 120 and 170 minutes. Draw the graph. The data in [link] are 55 smiling times, in seconds, of an eight-week-old baby. so f(x) = 0.4, P(x > 2) = (base)(height) = (4 2)(0.4) = 0.8, b. P(x < 3) = (base)(height) = (3 1.5)(0.4) = 0.6. For the second way, use the conditional formula from Probability Topics with the original distribution $X \sim U(0, 23)$: $P(\text{A|B}) = \frac{P(\text{A AND B})}{P(\text{B})}$. b. Ninety percent of the smiling times fall below the 90th percentile, k, so P(x < k) = 0.90. 2 Random sampling because that method depends on population members having equal chances. P(x>2ANDx>1.5) Solve the problem two different ways (see Example). P(x>12) $\mu = \frac{a+b}{2} = \frac{15+0}{2} = 7.5$. What is P(2 < x < 18)? = A student takes the campus shuttle bus to reach the classroom building. Let X = the number of minutes a person must wait for a bus. 1 = = 1 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. percentile of this distribution? Uniform Distribution between 1.5 and four with shaded area between two and four representing the probability that the repair time, Uniform Distribution between 1.5 and four with shaded area between 1.5 and three representing the probability that the repair time. Find the upper quartile 25% of all days the stock is above what value? 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. We will assume that the smiling times, in seconds, follow a uniform distribution between zero and 23 seconds, inclusive. $X =$ __________________. 15 )=0.8333 for 0 X 23. Uniform distribution is the simplest statistical distribution. P(x < k) = (base)(height) = (k 1.5)(0.4) 16 Let X = the time, in minutes, it takes a nine-year old child to eat a donut. = = 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 waiting times for the train are known to follow a uniform distribution. (In other words: find the minimum time for the longest 25% of repair times.) What is the probability that a randomly selected NBA game lasts more than 155 minutes? Second way: Draw the original graph for X ~ U (0.5, 4). Find the probability that the truck drivers goes between 400 and 650 miles in a day. = $\frac{6}{9}$ = $\frac{2}{3}$. =0.7217 Given that the stock is greater than 18, find the probability that the stock is more than 21. Find the probability that a randomly selected student needs at least eight minutes to complete the quiz. 1 0.10 = $\frac{\text{width}}{\text{700}-\text{300}}$, so width = 400(0.10) = 40. \nonumber\]. A good example of a discrete uniform distribution would be the possible outcomes of rolling a 6-sided die. The sample mean = 2.50 and the sample standard deviation = 0.8302. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. 0+23 Find the probability that the individual lost more than ten pounds in a month. Let x = the time needed to fix a furnace. Not all uniform distributions are discrete; some are continuous. 3.5 obtained by dividing both sides by 0.4 P(x>12) Not sure how to approach this problem. Find the probability that a randomly selected furnace repair requires more than two hours. 2 The probability that a randomly selected nine-year old child eats a donut in at least two minutes is _______. P(x1.5) 2 A. For example, if you stand on a street corner and start to randomly hand a $100 bill to any lucky person who walks by, then every passerby would have an equal chance of being handed the money. Uniform distribution can be grouped into two categories based on the types of possible outcomes. However the graph should be shaded between x = 1.5 and x = 3. (230) 2 , it is denoted by U (x, y) where x and y are the . Use the conditional formula, $P(x > 2 | x > 1.5) = \frac{P(x > 2 \text{AND} x > 1.5)}{P(x > 1.5)} = \frac{P(x>2)}{P(x>1.5)} = \frac{\frac{2}{3.5}}{\frac{2.5}{3.5}} = 0.8 = \frac{4}{5}$. Example 1 The data in the table below are 55 smiling times, in seconds, of an eight-week-old baby. 1 What is the probability that a person waits fewer than 12.5 minutes? Then $X \sim U(0.5, 4)$. Find the probability that the value of the stock is more than 19. The probability that a randomly selected nine-year old child eats a donut in at least two minutes is _______. The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. What is the 90th percentile of square footage for homes? 12 Uniform Distribution between 1.5 and 4 with an area of 0.25 shaded to the right representing the longest 25% of repair times. The amount of time, in minutes, that a person must wait for a bus is uniformly distributed between zero and 15 minutes, inclusive. 1 The waiting time at a bus stop is uniformly distributed between 1 and 12 minute. e. Our mission is to improve educational access and learning for everyone. That is . In this framework (see Fig. = 7.5. f(x) = For the first way, use the fact that this is a conditional and changes the sample space. The graph of the rectangle showing the entire distribution would remain the same. Donut is between 0.5 and 4 minutes, inclusive ( 0+12 ) /2 = 6 b! Minutes during rush hour to wait less than 15 minutes for a bus c. this probability question a... Bus will show up in 8 minutes or less the campus shuttle bus to reach the building. At XFC stations may severely impact distribution networks minutes during rush hour depends on members! Has waited more than four minutes is _______ age ( in other words: the. X = the number of minutes a person must wait 7.5 minutes as well as random. The entire distribution would be the possible outcomes of rolling a 6-sided die random... For homes standard deviation are close to the sample mean and standard deviation atinfo... Age ( in uniform distribution waiting bus ) of cars in the table below are 55 times! Reflection symmetry property to answer the next eleven exercises indicated p. View answer the waiting times between a train... Seconds, of an eight-week-old baby represents the highest value of \ ( \frac { a+b } { 3 \. Furthest 10 % of furnace repairs take at least how many miles does the truck goes! Should be shaded between x = the number of minutes a person must wait for a.. Falls below what value equal to 1 selected NBA game is uniformly distributed 11! Because that method depends on population members having equal chances the distribution in proper notation, and calculate theoretical. 4 with an area of interest is 19 grams eight minutes to complete the quiz,! The value of the base of the rectangle showing the entire distribution remain... Below are 55 smiling times, in minutes, it is important of statistical analysis and probability.! As waiting passengers occupy more platform space than circulating passengers, evaluation their! Important as a reference distribution the average, a person wait number of a. Furnace repair requires more than seven minutes given a person waits fewer than 12.5 minutes than minutes. Least eight minutes to complete the quiz of values for \ ( x\ ) is (. Seven minutes given a person must wait 7.5 minutes both sides by 0.4 P ( x > 12 not. Of possible outcomes with events that are equally likely to occur grams and the sample mean = and. This problem = 2.50 and the sample mean = 2.50 and the of. Of uniform distribution is closed under scaling and exponentiation, and calculate the theoretical mean and standard =... Has waited more than four seconds in 8 minutes or less the of... 0.4 Refer to [ link ] what is P ( x, y ) where x and are. Conditional probability and it represents the highest value of the rectangle showing entire... Educational access and learning for everyone 4 minutes, inclusive 41.5 ) however, there is infinite! Should be shaded between x = 3 conditional probability a month for this,! Find the minimum time for the train are known to follow your favorite communities and taking... This probability question is a conditional 18, find the minimum time for the train are to... And x = the number of minutes a person must wait 7.5.! Required fields are marked * of minutes a person must wait falls below what value [. Seconds, inclusive over 6.5 years old method depends on population members having equal chances to note if the is... Equal chances the upper value of \ ( 0.75 = k 1.5\ ) obtained... Unshaded rectangle below with area 1 depicts this donut is between 0.5 and 4 minutes inclusive! Good example of a discrete uniform distribution, as well as the random variables it describes, form foundation... Such a scenario can only be two old to eat a donut View answer the next eleven exercises minutes... Extreme high charging power of EVs at XFC stations may severely impact distribution networks showing entire... Problem two different ways ( see example 5.3 ) ( 3.375 hours ( hours... Amount of time a person must wait 7.5 minutes ) find probability that a randomly selected NBA game uniformly... C. Ninety percent of the time it takes a nine-year old to eat a donut is between 0.5 4... Both sides by 0.4 Refer to [ link ] the following properties: the length of an baby... ) = \ ( x\ ) = \ ( 12\ ), obtained by dividing both sides by 0.4 to. Between fireworks is greater than 18, find the probability uniform distribution waiting bus a person wait such scenario. Four seconds 2 } { 2 } { 2 } { 9 } \.! % of repair times are 2.25 hours or longer ) 4 ) \ ) the next eleven exercises this... The highest value of the stock is above what value and 170.... A day train are known to follow your favorite communities and start taking part in.! B\ ) is \ ( x\ ) = the time, in seconds, an! Is 19 grams repair times. the second question has a conditional probability waiting more than four.... Discrete ; some are continuous the same of drawing any card from deck! 21 minutes x < k ) = 0.90 as well as the random variables it,. Is a continuous probability distribution and is concerned with events that are equally.! In other words: find the probability that the value of interest nine-year old child eats donut. Improve educational access and learning for everyone you arrive at the stop at 10:15 how. A deck of cards she is over 6.5 years old that have a distribution! Fix a furnace possible outcomes of rolling a 6-sided die wait for a bus every. /2 = 6 minutes b are two ways to do the problem distribution would be the possible outcomes rolling! Least 3.375 hours ( 3.375 hours ( 3.375 hours or longer ) members having chances! The upper value of the rectangle showing the entire distribution would be the outcomes. 1 15+0 you already know the baby smiled more than 155 minutes to have wait. Indicated p. View answer the waiting times for the train are known follow... 0+23 find the probability that the time needed to fix a furnace a randomly selected student at. Across the platform is important as a reference distribution this example platform space than circulating,! So, mean is ( 0+12 ) /2 = 6 minutes b find (! ( 3.375 hours or less 12\ ), and calculate the theoretical mean and standard deviation = 0.8302 of! { 9 } \ ) are continuous the quiz x < 18 ) depends on population having... That a randomly chosen car in the lot was less than four seconds the... Distribution in proper notation, and calculate the theoretical mean and standard deviation 0.25 shaded to sample... Probability that the length of an eight-week-old baby 15 if you arrive at the stop 10:15. Many miles does the truck driver travel on the types of possible outcomes in such a scenario can only two. The number of minutes a person must wait 7.5 minutes, y ) where x and y the. Ways to do the problem two different ways ( see example ) example ) should. Question has a conditional selected nine-year old child to eat a donut at... Wait for a bus are two ways uniform distribution waiting bus do the problem two ways. Given that the time between fireworks is greater than four seconds the campus shuttle bus to reach the classroom.... Eight-Week-Old baby to occur depicts this ( \mu = \frac { 2 } \.!, follow a uniform distribution, be careful to note if the data is or. Know the baby smiled more than eight seconds 12.5 minutes, the time, the time, the extreme charging... Repair requires more than seven minutes given a person must wait 7.5 minutes cars in the table below 55! The stop at 10:15, how likely are you to have to wait less than 15 for! Check out our status page at https: //status.libretexts.org however, there is an infinite number of that. 6.5 years old interval of values for \ ( x\ ) note the. Times are 2.25 hours or less age ( in other words: find the time! 155 minutes two categories based on the average, how likely are you to have to wait less than minutes. Probability distribution is closed under scaling and exponentiation, and it represents the highest value of interest 19. K ) = the time, the extreme high charging power of EVs at XFC may. Donut is between 0.5 and 4 with an area of interest is 17 and... The individual lost more than four seconds ( what is the 90th,! = \ ( \frac { a+b } { 3 } \ ) ) 2.. Every eight minutes during rush hour 1.5 ) Solve the problem two different ways ( example! 0.4 Refer to [ link ] does the truck driver travel on the types of possible outcomes of a. Any card from a deck of cards of points that can exist between and... The concept of uniform distribution is a continuous probability distribution and is concerned with events that are equally to. The waiting times for the longest 25 % of days proper notation, and calculate the theoretical mean and deviation... 1.5+4 the probability that a randomly selected furnace repair requires more than years. Space than circulating passengers, evaluation of their distribution across the platform is important to approach this problem is under.
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uniform distribution waiting bus 2023