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. 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 uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. Another example of a uniform distribution is when a coin is tossed. The area must be 0.25, and 0.25 = (width)\(\left(\frac{1}{9}\right)\), so width = (0.25)(9) = 2.25. Suppose the time it takes a nine-year old to eat a donut is between 0.5 and 4 minutes, inclusive. Find the third quartile of ages of cars in the lot. ( Sixty percent of commuters wait more than how long for the train? The longest 25% of furnace repairs take at least 3.375 hours (3.375 hours or longer). The amount of time, in minutes, that a person must wait for a bus is uniformly distributed between zero and 15 minutes, inclusive. Darker shaded area represents P(x > 12). Discrete uniform distributions have a finite number of outcomes. So, mean is (0+12)/2 = 6 minutes b. Find the probability that the value of the stock is more than 19. What is the probability density function? 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. a+b 23 There are several ways in which discrete uniform distribution can be valuable for businesses. 12 The data that follow are the square footage (in 1,000 feet squared) of 28 homes. Find the probability that the commuter waits between three and four minutes. A form of probability distribution where every possible outcome has an equal likelihood of happening. k=(0.90)(15)=13.5 P(2 < x < 18) = (base)(height) = (18 2)\(\left(\frac{1}{23}\right)\) = \(\left(\frac{16}{23}\right)\). For example, we want to predict the following: The amount of timeuntilthe customer finishes browsing and actually purchases something in your store (success). Shade the area of interest. We recommend using a It is generally denoted by u (x, y). P(x>1.5) Department of Earth Sciences, Freie Universitaet Berlin. The uniform distribution is a probability distribution in which every value between an interval from a to b is equally likely to occur. = = Below is the probability density function for the waiting time. P(x>1.5) 1 When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive. 2 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. f(x) = \(\frac{1}{b-a}\) for a x b. Suppose the time it takes a student to finish a quiz is uniformly distributed between six and 15 minutes, inclusive. 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. =0.7217 Find the 90thpercentile. \(f(x) = \frac{1}{15-0} = \frac{1}{15}\) for \(0 \leq x \leq 15\). Let \(X =\) the time needed to change the oil on a car. 11 Find the probability that a randomly chosen car in the lot was less than four years old. P(x>2) Refer to [link]. What is P(2 < x < 18)? Uniform Distribution. 1 5. The probability \(P(c < X < d)\) may be found by computing the area under \(f(x)\), between \(c\) and \(d\). Find the probability that the time is at most 30 minutes. However, there is an infinite number of points that can exist. 1 So, \(P(x > 12|x > 8) = \frac{(x > 12 \text{ AND } x > 8)}{P(x > 8)} = \frac{P(x > 12)}{P(x > 8)} = \frac{\frac{11}{23}}{\frac{15}{23}} = \frac{11}{15}\). ba Press J to jump to the feed. b. Then X ~ U (0.5, 4). It is _____________ (discrete or continuous). Suppose the time it takes a student to finish a quiz is uniformly distributed between six and 15 minutes, inclusive. Then \(X \sim U(0.5, 4)\). Draw the graph of the distribution for \(P(x > 9)\). Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . (b-a)2 15 and you must attribute OpenStax. What is the probability that the duration of games for a team for the 2011 season is between 480 and 500 hours? Find the 90th percentile. a. 2 Your starting point is 1.5 minutes. First, I'm asked to calculate the expected value E (X). = Example 1 The data in the table below are 55 smiling times, in seconds, of an eight-week-old baby. 1 What are the constraints for the values of x? P(x>1.5) 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. a+b The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. Heres how to visualize that distribution: And the probability that a randomly selected dolphin weighs between 120 and 130 pounds can be visualized as follows: The uniform distribution has the following properties: We could calculate the following properties for this distribution: Use the following practice problems to test your knowledge of the uniform distribution. ) Waiting time for the bus is uniformly distributed between [0,7] (in minutes) and a person will use the bus 145 times per year. Find the probability that the time is more than 40 minutes given (or knowing that) it is at least 30 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 waiting passengers occupy more platform space than circulating passengers, evaluation of their distribution across the platform is important. \(P\left(x
12\)) and \(\text{B}\) is (\(x > 8\)). P(x>8) To keep advancing your career, the additional CFI resources below will be useful: A free, comprehensive best practices guide to advance your financial modeling skills, Get Certified for Business Intelligence (BIDA). The distribution can be written as \(X \sim U(1.5, 4.5)\). 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. are not subject to the Creative Commons license and may not be reproduced without the prior and express written P(x 1.5 Department. Long for the train 1.5, 4.5 ) \ ) for a team for the train their. Waits more than 12 seconds knowing that the value of the stock is more than 19 arrived the... Probability of waiting more than how long for the waiting time for the bus... Or longer ) the theoretical mean and standard deviation are this problem, the time needed to change the in. 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