Then x ~ U (1.5, 4). (a, b)). f (x) = 1 (23 âˆ’ 0) More about the uniform distribution probability. 15 P(x>12) 0.90=( ) 12 The 30th percentile of repair times is 2.25 hours. P(x > k) = 0.25 Find the probability that a randomly selected student needs at least eight minutes to complete the quiz. 16 2 Darker shaded area represents P(x > 12). P(x>8) = 11.50 seconds and σ = μ= = = 15 μ= then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a digital format, 0.625 = 4 − k,   What is the probability that a randomly chosen eight-week-old baby smiles between two and 18 seconds? Let X = the time needed to change the oil on a car. b. Ninety percent of the smiling times fall below the 90th percentile, k, so P(x < k) = 0.90. 1 5 The continuous uniform distribution on an interval of \( \R \) is one of the simplest of all probability distributions, but nonetheless very important. For the first way, use the fact that this is a conditional and changes the sample space. 2 Let x = the time needed to fix a furnace. 4 P(x>1.5) μ Let X = the time, in minutes, it takes a student to finish a quiz. ) σ= 1 = 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 4545. c. Ninety percent of the time, the time a person must wait falls below what value? 15 The sample mean = 7.9 and the sample standard deviation = 4.33. P(x>8) This means that any smiling time from zero to and including 23 seconds is equally likely. The probability density function is The The following is the plot of the uniform probability density function. Find P(x > 12|x > 8) There are two ways to do the problem. (k−0)( 15 The Standard deviation is 4.3 minutes. )=0.90, k=( 1 = You already know the baby smiled more than eight seconds. a. We will assume that the smiling times, in seconds, follow a uniform distribution between zero and 23 seconds, inclusive. 1 1 1 (b−a) c. Find the 90th percentile. b−a What is the probability that the duration of games for a team for the 2011 season is between 480 and 500 hours? 1 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. a. =0.8= 5 σ = 2 σ= )( expressed in terms of the standard We recommend using a When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive of endpoints. = 2 15 The following is the plot of the uniform percent point function. 23 = 1.5+4 3.5 \( Z(p) = 1 - p \;\;\;\;\;\;\; \mbox{for} \ 0 \le p \le 1 \). 12 2 You must reduce the sample space. 23 4 âˆ’ 1.5 The following is the plot of the uniform survival function. 1 12 15 Let X = the time, in minutes, it takes a nine-year old child to eat a donut. The probability a person waits less than 12.5 minutes is 0.8333. b. ( ( ) Creative Commons Attribution License 4.0 license. 1 The following is the plot of the uniform inverse survival function. 12= P(x>2) P(B) Find the probability that a randomly selected furnace repair requires less than three hours. 2.5 Here is a little bit of information about the uniform distribution probability so you can better use the the probability calculator presented above: The uniform distribution is a type of continuous probability distribution that can take random values on the the interval \([a, b]\), and it zero outside of this interval. 23−0 Entire shaded area shows P(x > 8). The notation for the uniform distribution is. = 7.5. 3.5 15 Except where otherwise noted, textbooks on this site P(x>2 AND x>1.5) The distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds. = )=20.7 expressed in terms of the standard a+b =45. random number generators generate random numbers on the (0,1) 1 12 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. 2 11 k=( The uniform distribution corresponds to picking a point at random from the interval. distribution, all subsequent formulas in this section are (23 âˆ’ 0) 1 (b−a) (b-a)2 15. P(x>2 AND x>1.5) This book is Creative Commons Attribution License The graph illustrates the new sample space. P(A AND B) Find the probability that a randomly selected furnace repair requires more than two hours. = 4−1.5 interval. b. = For this reason, it is important as a reference distribution. You are asked to find 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. = 4−1.5 For this example, X ~ U(0, 23) and f(x) = The total duration of baseball games in the major league in the 2011 season is uniformly distributed between 447 hours and 521 hours inclusive. ) 1 (k−0)( The second question has a conditional probability. P(A AND B)

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