If the probability density function or probability distribution of a uniform . obtained by dividing both sides by 0.4 \(P(x < 4 | x < 7.5) =\) _______. percentile of this distribution? It is generally represented by u (x,y). 0.90 16 consent of Rice University. Let \(X =\) the time, in minutes, it takes a nine-year old child to eat a donut. The shuttle bus arrives at his stop every 15 minutes but the actual arrival time at the stop is random. 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. What is P(2 < x < 18)? 1 Find the probability that she is over 6.5 years old. . P(2 < x < 18) = 0.8; 90th percentile = 18. Solution 3: The minimum weight is 15 grams and the maximum weight is 25 grams. Creative Commons Attribution License A continuous uniform distribution is a statistical distribution with an infinite number of equally likely measurable values. (ba) When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive. However, there is an infinite number of points that can exist. X = The age (in years) of cars in the staff parking lot. A. A fireworks show is designed so that the time between fireworks is between one and five seconds, and follows a uniform distribution. 1 Sketch the graph, and shade the area of interest. ( Then \(X \sim U(0.5, 4)\). \(k = (0.90)(15) = 13.5\) Find the third quartile of ages of cars in the lot. What has changed in the previous two problems that made the solutions different? Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . P(x
12 | x > 8) = (23 12)\left(\frac{1}{15}\right) = \left(\frac{11}{15}\right)\). To find f(x): f (x) = In statistics and probability theory, a discrete uniform distribution is a statistical distribution where the probability of outcomes is equally likely and with finite values. For example, we want to predict the following: The amount of timeuntilthe customer finishes browsing and actually purchases something in your store (success). Sketch the graph of the probability distribution. Want to cite, share, or modify this book? 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. = \(\frac{0\text{}+\text{}23}{2}\) 14.42 C. 9.6318 D. 10.678 E. 11.34 Question 10 of 20 1.0/ 1.0 Points The waiting time for a bus has a uniform distribution between 2 and 11 minutes. Let \(X =\) the time, in minutes, it takes a student to finish a quiz. Suppose the time it takes a nine-year old to eat a donut is between 0.5 and 4 minutes, inclusive. X is now asked to be the waiting time for the bus in seconds on a randomly chosen trip. Formulas for the theoretical mean and standard deviation are, \[\sigma = \sqrt{\frac{(b-a)^{2}}{12}} \nonumber\], For this problem, the theoretical mean and standard deviation are, \[\mu = \frac{0+23}{2} = 11.50 \, seconds \nonumber\], \[\sigma = \frac{(23-0)^{2}}{12} = 6.64\, seconds. 15.67 B. We are interested in the weight loss of a randomly selected individual following the program for one month. for 0 x 15. 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). 0.25 = (4 k)(0.4); Solve for k: a+b \(f(x) = \frac{1}{4-1.5} = \frac{2}{5}\) for \(1.5 \leq x \leq 4\). = What is the expected waiting time? 4 Your starting point is 1.5 minutes. This is a modeling technique that uses programmed technology to identify the probabilities of different outcomes. In statistics, uniform distribution is a probability distribution where all outcomes are equally likely. = What has changed in the previous two problems that made the solutions different. looks like this: f (x) 1 b-a X a b. Uniform Distribution between 1.5 and 4 with an area of 0.25 shaded to the right representing the longest 25% of repair times. 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. 3.375 hours is the 75th percentile of furnace repair times. Draw the graph of the distribution for P(x > 9). It means that the value of x is just as likely to be any number between 1.5 and 4.5. 41.5 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. The waiting times for the train are known to follow a uniform distribution. We write X U(a, b). 1 It is assumed that the waiting time for a particular individual is a random variable with a continuous uniform distribution. = A subway train on the Red Line arrives every eight minutes during rush hour. \(X =\) __________________. b. Theres only 5 minutes left before 10:20. 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. a. If you are redistributing all or part of this book in a print format, c. This probability question is a conditional. In this distribution, outcomes are equally likely. The sample mean = 7.9 and the sample standard deviation = 4.33. Ninety percent of the time, a person must wait at most 13.5 minutes. Example 5.2 The 30th percentile of repair times is 2.25 hours. 16 What is P(2 < x < 18)? = Find the probability that a bus will come within the next 10 minutes. f(X) = 1 150 = 1 15 for 0 X 15. Let X = the time needed to change the oil on a car. Uniform Distribution between 1.5 and 4 with an area of 0.30 shaded to the left, representing the shortest 30% of repair times. What is the 90th percentile of square footage for homes? )=20.7. for 1.5 x 4. 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. 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 times for the train are known to follow a uniform distribution. ) (b-a)2 Post all of your math-learning resources here. The lower value of interest is 155 minutes and the upper value of interest is 170 minutes. The waiting times for the train are known to follow a uniform distribution. P(X > 19) = (25 19) \(\left(\frac{1}{9}\right)\) 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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Of different outcomes 11 this means that any smiling time from zero to and including 23 seconds is equally to... 1 150 = 1 15 for 0 x 15 2 Write the probability that he less. License a continuous probability distribution and is concerned with events that are equally likely Post all of your math-learning here.
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