Want to cite, share, or modify this book? ( 1 Posted at 09:48h in michael deluise matt leblanc by Continuous Uniform Distribution - Waiting at the bus stop 1,128 views Aug 9, 2020 20 Dislike Share The A Plus Project 331 subscribers This is an example of a problem that can be solved with the. Let k = the 90th percentile. The data in [link] are 55 smiling times, in seconds, of an eight-week-old baby. 2 Find the probability that the value of the stock is more than 19. Then \(x \sim U(1.5, 4)\). The longest 25% of furnace repairs take at least 3.375 hours (3.375 hours or longer). 2 Monte Carlo simulation is often used to forecast scenarios and help in the identification of risks. The answer for 1) is 5/8 and 2) is 1/3. 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. I was originally getting .75 for part 1 but I didn't realize that you had to subtract P(A and B). 0+23 The distribution can be written as \(X \sim U(1.5, 4.5)\). P(x>8) a+b If so, what if I had wait less than 30 minutes? X = a real number between a and b (in some instances, X can take on the values a and b). c. Ninety percent of the time, the time a person must wait falls below what value? 2 P(x < k) = (base)(height) = (k 1.5)(0.4) Let \(X =\) the time, in minutes, it takes a nine-year old child to eat a donut. One of the most important applications of the uniform distribution is in the generation of random numbers. Create an account to follow your favorite communities and start taking part in conversations. 30% of repair times are 2.25 hours or less. A random number generator picks a number from one to nine in a uniform manner. ( \[P(x < k) = (\text{base})(\text{height}) = (12.50)\left(\frac{1}{15}\right) = 0.8333\]. For this example, X ~ U(0, 23) and f(x) = \(\frac{1}{23-0}\) for 0 X 23. Answer: (Round to two decimal place.) Suppose the time it takes a student to finish a quiz is uniformly distributed between six and 15 minutes, inclusive. The longest 25% of furnace repair times take at least how long? P(AANDB) I'd love to hear an explanation for these answers when you get one, because they don't make any sense to me. a. b is 12, and it represents the highest value of x. ) obtained by subtracting four from both sides: k = 3.375 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. Then X ~ U (0.5, 4). 1 = 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. then you must include on every digital page view the following attribution: Use the information below to generate a citation. \(b\) is \(12\), and it represents the highest value of \(x\). 15.67 B. This module describes the properties of the Uniform Distribution which describes a set of data for which all aluesv have an equal probabilit.y Example 1 . What percentile does this represent? 30% of repair times are 2.5 hours or less. The 30th percentile of repair times is 2.25 hours. pdf: \(f(x) = \frac{1}{b-a}\) for \(a \leq x \leq b\), standard deviation \(\sigma = \sqrt{\frac{(b-a)^{2}}{12}}\), \(P(c < X < d) = (d c)\left(\frac{1}{b-a}\right)\). Get started with our course today. Find the probability that a person is born at the exact moment week 19 starts. 2 P(x>1.5) Find the upper quartile 25% of all days the stock is above what value? Your starting point is 1.5 minutes. If X has a uniform distribution where a < x < b or a x b, then X takes on values between a and b (may include a and b). )=0.90, k=( ( What is the probability that the waiting time for this bus is less than 5.5 minutes on a given day? The 90th percentile is 13.5 minutes. 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. Write the distribution in proper notation, and calculate the theoretical mean and standard deviation. \(k = (0.90)(15) = 13.5\) Sketch the graph of the probability distribution. Solve the problem two different ways (see Example 5.3). \(P(x > k) = 0.25\) In words, define the random variable \(X\). = Uniform distribution can be grouped into two categories based on the types of possible outcomes. =45. Suppose it is known that the individual lost more than ten pounds in a month. a. hours and \(\sigma =\sqrt{\frac{{\left(41.5\right)}^{2}}{12}}=0.7217\) hours. The probability that a randomly selected nine-year old child eats a donut in at least two minutes is _______. 4 ) Find the probability that a randomly selected furnace repair requires more than two hours. The data follow a uniform distribution where all values between and including zero and 14 are equally likely. Second way: Draw the original graph for X ~ U (0.5, 4). The waiting times for the train are known to follow a uniform distribution. The waiting times for the train are known to follow a uniform distribution. Let X = the time, in minutes, it takes a student to finish a quiz. 23 f(x) = Find the probability that the truck drivers goes between 400 and 650 miles in a day. What is the probability that a person waits fewer than 12.5 minutes? 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. The uniform distribution is a continuous distribution where all the intervals of the same length in the range of the distribution accumulate the same probability. c. This probability question is a conditional. P(0 < X < 8) = (8-0) / (20-0) = 8/20 =0.4. Draw a graph. The student allows 10 minutes waiting time for the shuttle in his plan to make it in time to the class.a. = 1 \(X =\) a real number between \(a\) and \(b\) (in some instances, \(X\) can take on the values \(a\) and \(b\)). Correct answers: 3 question: The waiting time for a bus has a uniform distribution between 0 and 8 minutes. 3.375 = k, Find the indicated p. View Answer The waiting times between a subway departure schedule and the arrival of a passenger are uniformly. You must reduce the sample space. 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. Write the probability density function. P(x>8) The time follows a uniform distribution. The probability that a randomly selected nine-year old child eats a donut in at least two minutes is _______. Question 1: A bus shows up at a bus stop every 20 minutes. Entire shaded area shows P(x > 8). To find f(x): f (x) = \(\frac{1}{4\text{}-\text{}1.5}\) = \(\frac{1}{2.5}\) 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. \nonumber\]. = (ba) 1 Random sampling because that method depends on population members having equal chances. =0.8= As the question stands, if 2 buses arrive, that is fine, because at least 1 bus arriving is satisfied. For the second way, use the conditional formula from Probability Topics with the original distribution \(X \sim U(0, 23)\): \(P(\text{A|B}) = \frac{P(\text{A AND B})}{P(\text{B})}\). Let \(X =\) the time, in minutes, it takes a student to finish a quiz. To find \(f(x): f(x) = \frac{1}{4-1.5} = \frac{1}{2.5}\) so \(f(x) = 0.4\), \(P(x > 2) = (\text{base})(\text{height}) = (4 2)(0.4) = 0.8\), b. 23 The Structured Query Language (SQL) comprises several different data types that allow it to store different types of information What is Structured Query Language (SQL)? What is the 90th . 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 \(\frac{4}{5}\). A continuous uniform distribution (also referred to as rectangular distribution) is a statistical distribution with an infinite number of equally likely measurable values. a= 0 and b= 15. Question 2: The length of an NBA game is uniformly distributed between 120 and 170 minutes. \(0.90 = (k)\left(\frac{1}{15}\right)\) Continuous Uniform Distribution Example 2 When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive of endpoints. Uniform Distribution. The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. (In other words: find the minimum time for the longest 25% of repair times.) Then x ~ U (1.5, 4). Plume, 1995. 230 If you are waiting for a train, you have anywhere from zero minutes to ten minutes to wait. ) 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. a person has waited more than four minutes is? Draw a graph. )( OR. The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. 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. 2 What is the 90th percentile of square footage for homes? A distribution is given as \(X \sim U(0, 20)\). P (x < k) = 0.30 b. The sample mean = 11.65 and the sample standard deviation = 6.08. for 0 x 15. The possible outcomes in such a scenario can only be two. P(x > k) = (base)(height) = (4 k)(0.4) Example The data in the table below are 55 smiling times, in seconds, of an eight-week-old baby. = \(\frac{15\text{}+\text{}0}{2}\) Suppose that you arrived at the stop at 10:00 and wait until 10:05 without a bus arriving. The histogram that could be constructed from the sample is an empirical distribution that closely matches the theoretical uniform distribution. 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. 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