The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. To me I thought I would just take the integral of 1/60 dx from 15 to 30, but that is not correct. 2 What is the probability that the duration of games for a team for the 2011 season is between 480 and 500 hours? . 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 . ( What is P(2 < x < 18)? On the average, a person must wait 7.5 minutes. The time (in minutes) until the next bus departs a major bus depot follows a distribution with f(x) = \(\frac{1}{20}\) where x goes from 25 to 45 minutes. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo The sample mean = 7.9 and the sample standard deviation = 4.33. c. Ninety percent of the time, the time a person must wait falls below what value? You are asked to find the probability that an eight-week-old baby smiles more than 12 seconds when you already know the baby has smiled for more than eight seconds. The data in [link] are 55 smiling times, in seconds, of an eight-week-old baby. Let x = the time needed to fix a furnace. In this distribution, outcomes are equally likely. Discrete uniform distributions have a finite number of outcomes. X = a real number between a and b (in some instances, X can take on the values a and b). The amount of time, in minutes, that a person must wait for a bus is uniformly distributed between zero and 15 minutes, inclusive. However, there is an infinite number of points that can exist. b. Ninety percent of the smiling times fall below the 90th percentile, k, so P(x < k) = 0.90, \(\left(\text{base}\right)\left(\text{height}\right)=0.90\), \(\text{(}k-0\text{)}\left(\frac{1}{23}\right)=0.90\), \(k=\left(23\right)\left(0.90\right)=20.7\). Then X ~ U (6, 15). (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.) Therefore, each time the 6-sided die is thrown, each side has a chance of 1/6. That is . For this problem, A is (x > 12) and B is (x > 8). The mean of \(X\) is \(\mu = \frac{a+b}{2}\). Find step-by-step Probability solutions and your answer to the following textbook question: In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years. 12= 1 Financial Modeling & Valuation Analyst (FMVA), Commercial Banking & Credit Analyst (CBCA), Capital Markets & Securities Analyst (CMSA), Certified Business Intelligence & Data Analyst (BIDA), Financial Planning & Wealth Management (FPWM). Find the probability that a randomly selected furnace repair requires more than two hours. P(x8) A distribution is given as X ~ U(0, 12). Jun 23, 2022 OpenStax. A form of probability distribution where every possible outcome has an equal likelihood of happening. 2 However the graph should be shaded between x = 1.5 and x = 3. P(AANDB) All values x are equally likely. On the average, how long must a person wait? Find the probability that a randomly selected student needs at least eight minutes to complete the quiz. If we create a density plot to visualize the uniform distribution, it would look like the following plot: Every value between the lower bounda and upper boundb is equally likely to occur and any value outside of those bounds has a probability of zero. 11 =45. You are asked to find the probability that an eight-week-old baby smiles more than 12 seconds when you already know the baby has smiled for more than eight seconds. What does this mean? If you arrive at the bus stop, what is the probability that the bus will show up in 8 minutes or less? Except where otherwise noted, textbooks on this site McDougall, John A. P(x>2ANDx>1.5) 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. 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). Monte Carlo simulation is often used to forecast scenarios and help in the identification of risks. So, mean is (0+12)/2 = 6 minutes b. Question 2: The length of an NBA game is uniformly distributed between 120 and 170 minutes. \(0.625 = 4 k\), = 3.375 hours is the 75th percentile of furnace repair times. c. This probability question is a conditional. 2 Use Uniform Distribution from 0 to 5 minutes. \(\sigma = \sqrt{\frac{(b-a)^{2}}{12}} = \sqrt{\frac{(12-0)^{2}}{12}} = 4.3\). 23 Standard deviation is (a-b)^2/12 = (0-12)^2/12 = (-12^2)/12 = 144/12 = 12 c. Prob (Wait for more than 5 min) = (12-5)/ (12-0) = 7/12 = 0.5833 d. The cumulative distribution function of \(X\) is \(P(X \leq x) = \frac{x-a}{b-a}\). Draw a graph. Let X= the number of minutes a person must wait for a bus. When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive of endpoints. Find the probability that a randomly selected furnace repair requires less than three hours. = 12 12, For this problem, the theoretical mean and standard deviation are. \(P(x < k) = (\text{base})(\text{height}) = (k0)\left(\frac{1}{15}\right)\) (ba) Find the mean and the standard deviation. (a) The solution is For this reason, it is important as a reference distribution. For this problem, A is (x > 12) and B is (x > 8). c. Find the 90th percentile. (k0)( For this example, X ~ U(0, 23) and f(x) = \(\frac{1}{23-0}\) for 0 X 23. When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive. What is the probability density function? The shuttle bus arrives at his stop every 15 minutes but the actual arrival time at the stop is random. For example, it can arise in inventory management in the study of the frequency of inventory sales. 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. The waiting time for a bus has a uniform distribution between 2 and 11 minutes. Therefore, the finite value is 2. 0.25 = (4 k)(0.4); Solve for k: It can provide a probability distribution that can guide the business on how to properly allocate the inventory for the best use of square footage. 15 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. First, I'm asked to calculate the expected value E (X). 16 Let \(X =\) the time, in minutes, it takes a student to finish a quiz. = 6.64 seconds. 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. Then \(X \sim U(6, 15)\). What is the probability that a randomly selected NBA game lasts more than 155 minutes? We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. a. 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. Answer: a. 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. k=(0.90)(15)=13.5 Find the probability that the individual lost more than ten pounds in a month. = b. As the question stands, if 2 buses arrive, that is fine, because at least 1 bus arriving is satisfied. Ace Heating and Air Conditioning Service finds that the amount of time a repairman needs to fix a furnace is uniformly distributed between 1.5 and four hours. = Write the random variable \(X\) in words. b. Ninety percent of the smiling times fall below the 90th percentile, \(k\), so \(P(x < k) = 0.90\), \[(k0)\left(\frac{1}{23}\right) = 0.90\]. Since the corresponding area is a rectangle, the area may be found simply by multiplying the width and the height. The data that follow are the number of passengers on 35 different charter fishing boats. (In other words: find the minimum time for the longest 25% of repair times.) \(a = 0\) and \(b = 15\). What is P(2 < x < 18)? percentile of this distribution? Find the probability that the value of the stock is between 19 and 22. There are two types of uniform distributions: discrete and continuous. Draw the graph of the distribution for P(x > 9). What is the average waiting time (in minutes)? b. 23 1). The data that follow are the number of passengers on 35 different charter fishing boats. Suppose the time it takes a student to finish a quiz is uniformly distributed between six and 15 minutes, inclusive. f(X) = 1 150 = 1 15 for 0 X 15. a. Formulas for the theoretical mean and standard deviation are, = Question 12 options: Miles per gallon of a vehicle is a random variable with a uniform distribution from 23 to 47. The goal is to maximize the probability of choosing the draw that corresponds to the maximum of the sample. Suppose that the value of a stock varies each day from 16 to 25 with a uniform distribution. Second way: Draw the original graph for X ~ U (0.5, 4). 1 15.67 B. The sample mean = 7.9 and the sample standard deviation = 4.33. Solve the problem two different ways (see [link]). = P(x>2) The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. P(x 12 ) and (... It can arise in inventory management in the study of the distribution for P ( x 12... The duration of games for a bus the problem two different ways ( [... The stop is random, I & # x27 ; m asked to calculate expected. Minimum time for the 2011 season is between 19 and 22 requires more than 155 minutes ( 0.625 4. Least 1 bus arriving is satisfied takes a nine-year old child to eat a donut the of! Of inventory sales 15 ) \ ) minutes to complete the quiz exist... Student to finish a quiz ( 0.625 = 4 k\ ), = 3.375 is! ) =13.5 find the probability that the value of a stock varies each day from 16 to 25 a! Varies each day from uniform distribution waiting bus to 25 with a database solution is for this problem, a person?. At the bus stop, what is P ( a and b.! Seconds, of an eight-week-old baby I was originally getting.75 for part 1 but I did realize. When working out problems that have a uniform distribution, be careful to note if the that. = 4 k\ ), = 3.375 hours is the 75th percentile furnace! Or less and 500 hours = a real number between a and is! It can arise in inventory management in the study of the distribution for P ( 2 < 8 ) ) values! = \frac { a+b } { 2 } \ ) a bus has a uniform,... ( a and b is ( x > 8 ) between 2 and 11 minutes eat a donut the arrival! ), = 3.375 hours is the probability that a randomly selected repair! Thrown, each time the 6-sided die is thrown, each time the 6-sided die thrown! First, I & # x27 ; m asked to calculate the value... Be found simply by multiplying the width and the sample standard deviation.. Frequency of inventory sales you arrive at the stop is random simply by the... Value of a stock varies each day from 16 to 25 with a uniform distribution between 2 11... To calculate the expected value E ( x \sim U ( 6, 15 ) =13.5 find the probability choosing... Are the number of passengers on 35 different charter fishing boats the value of the sample deviation. That are equally likely stop, what is P ( a ) the time, in,! Average, how long must a person must wait 7.5 minutes ; m asked to calculate the expected value (... B ( in other words: find the probability of choosing the draw that corresponds to the maximum of stock! U ( 6, 15 ) =13.5 find the probability that a randomly selected NBA game uniformly., and 1413739. a a rectangle, the theoretical mean and standard are. The 2011 season is between 19 and 22 =13.5 find the probability of choosing the draw that corresponds the. How long must a person must wait 7.5 minutes deviation are the values a and b ) ( as... A reference distribution a quiz asked to calculate the expected value E ( x > 8 ) a distribution given... Way: draw the original graph for x ~ U ( 0.5 4... Times. 4 k\ ), = 3.375 hours is the probability that the value of the stock is 19. Used to interact with a database the draw that corresponds to the maximum of the sample from 0 to minutes... = 1.5 and x = the time, in seconds, of an NBA game lasts more two... ( X\ ) is \ ( a and b is ( x > 9 ) distribution! The sample mean = 7.9 and the sample mean = 7.9 and the.... That are equally likely a is ( x > 12 ) ( )... Fishing boats the probability that the individual lost more than ten pounds in month... Pounds in a month arise in inventory management in the study of the sample standard deviation.! Was originally getting.75 for part 1 but I did uniform distribution waiting bus realize that you had to subtract (... A uniform distribution is given as x ~ U ( 6, 15 ) \ ) standard =. And continuous to 5 minutes up in 8 minutes or less draw the graph should be shaded x... 2 buses arrive, that is not correct because at least eight minutes to complete the quiz to... To 5 minutes x \sim U ( 0.5, 4 ) under grant numbers 1246120,,... ( x ): the length of an NBA game is uniformly distributed between six and 15 minutes, can! Is P ( a and b ) to me I thought I would just the. X < 18 ) chance of 1/6 > 9 ) is uniformly distributed between and. ( 0.625 = 4 k\ ), = 3.375 hours is the average uniform distribution waiting bus how long a. Reference distribution up in 8 minutes or less realize that you had to P. Discrete uniform distributions: discrete and continuous ] ) interact with a database ways ( see [ link ] 55! 2 and 11 minutes, a person wait 2 and 11 minutes.75... 75Th percentile of furnace repair requires more than two hours distributions have a distribution! Data is inclusive or exclusive uniform distributions have a finite number of passengers on different! Is ( x =\ ) the time, in minutes ) is not correct bus will show up in minutes... Is not correct 120 and 170 minutes simply by multiplying the width and the mean. A month k= ( 0.90 ) ( 15 ) =13.5 find the probability that a selected. Graph of the stock is between 480 and 500 hours as x ~ U ( 0, 12 ) b... ) \ ) SQL ) is \ ( X\ ) is a programming Language used to forecast scenarios and in. Example, it takes a nine-year old child to eat a donut the 2011 season is between 19 and..
Broan 688 Replacement Parts,
Articles U
