The McDougall Program for Maximum Weight Loss. According to a study by Dr. John McDougall of his live-in weight loss program at St. Helena Hospital, the people who follow his program lose between six and 15 pounds a month until they approach trim body weight. 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. =0.8= To me I thought I would just take the integral of 1/60 dx from 15 to 30, but that is not correct. It is generally represented by u (x,y). Find the probability that the value of the stock is more than 19. The amount of timeuntilthe hardware on AWS EC2 fails (failure). b. Ninety percent of the smiling times fall below the 90th percentile, \(k\), so \(P(x < k) = 0.90\), \[(k0)\left(\frac{1}{23}\right) = 0.90\]. = \(\sqrt{\frac{\left(b-a{\right)}^{2}}{12}}=\sqrt{\frac{\left(\mathrm{15}-0{\right)}^{2}}{12}}\) = 4.3. The McDougall Program for Maximum Weight Loss. 0+23 \(\mu = \frac{a+b}{2} = \frac{15+0}{2} = 7.5\). The graph illustrates the new sample space. Define the random . The unshaded rectangle below with area 1 depicts this. Press question mark to learn the rest of the keyboard shortcuts. The percentage of the probability is 1 divided by the total number of outcomes (number of passersby). Public transport systems have been affected by the global pandemic Coronavirus disease 2019 (COVID-19). 1 for 0 X 23. Find the probability. OR. Answer Key:0.6 | .6| 0.60|.60 Feedback: Interval goes from 0 x 10 P (x < 6) = Question 11 of 20 0.0/ 1.0 Points In this distribution, outcomes are equally likely. The graph of the rectangle showing the entire distribution would remain the same. Find the third quartile of ages of cars in the lot. Find the 90th percentile. \(P(x < 3) = (\text{base})(\text{height}) = (3 1.5)(0.4) = 0.6\). = 1 The graph of the rectangle showing the entire distribution would remain the same. f (x) = = ) The graph illustrates the new sample space. P(x < k) = (base)(height) = (k 1.5)(0.4) If we randomly select a dolphin at random, we can use the formula above to determine the probability that the chosen dolphin will weigh between 120 and 130 pounds: The probability that the chosen dolphin will weigh between 120 and 130 pounds is0.2. What has changed in the previous two problems that made the solutions different? 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. Your email address will not be published. \(a =\) smallest \(X\); \(b =\) largest \(X\), The standard deviation is \(\sigma = \sqrt{\frac{(b-a)^{2}}{12}}\), Probability density function: \(f(x) = \frac{1}{b-a} \text{for} a \leq X \leq b\), Area to the Left of \(x\): \(P(X < x) = (x a)\left(\frac{1}{b-a}\right)\), Area to the Right of \(x\): P(\(X\) > \(x\)) = (b x)\(\left(\frac{1}{b-a}\right)\), Area Between \(c\) and \(d\): \(P(c < x < d) = (\text{base})(\text{height}) = (d c)\left(\frac{1}{b-a}\right)\), Uniform: \(X \sim U(a, b)\) where \(a < x < b\). 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. Question: The Uniform Distribution The Uniform Distribution is a Continuous Probability Distribution that is commonly applied when the possible outcomes of an event are bound on an interval yet all values are equally likely Apply the Uniform Distribution to a scenario The time spent waiting for a bus is uniformly distributed between 0 and 5 Plume, 1995. P(x > 21| x > 18). 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. 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. (ba) 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. P(x 2|x > 1.5) = \(\frac{P\left(x>2\text{AND}x>1.5\right)}{P\left(x>\text{1}\text{.5}\right)}=\frac{P\left(x>2\right)}{P\left(x>1.5\right)}=\frac{\frac{2}{3.5}}{\frac{2.5}{3.5}}=\text{0}\text{.8}=\frac{4}{5}\). P(B). Let \(X =\) the time, in minutes, it takes a nine-year old child to eat a donut. for 8 < x < 23, P(x > 12|x > 8) = (23 12) Draw the graph. 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. 16 In this distribution, outcomes are equally likely. What is the average waiting time (in minutes)? obtained by subtracting four from both sides: \(k = 3.375\) The probability of waiting more than seven minutes given a person has waited more than four minutes is? = (In other words: find the minimum time for the longest 25% of repair times.) k=(0.90)(15)=13.5 We will assume that the smiling times, in seconds, follow a uniform distribution between zero and 23 seconds, inclusive. c. Ninety percent of the time, the time a person must wait falls below what value? k = 2.25 , obtained by adding 1.5 to both sides Lets suppose that the weight loss is uniformly distributed. Ninety percent of the time, a person must wait at most 13.5 minutes. The histogram that could be constructed from the sample is an empirical distribution that closely matches the theoretical uniform distribution. (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.) Our mission is to improve educational access and learning for everyone. What is the 90th . 1 The second question has a conditional probability. When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive. 2 Find P(x > 12|x > 8) There are two ways to do the problem. = The sample mean = 11.49 and the sample standard deviation = 6.23. Suppose the time it takes a nine-year old to eat a donut is between 0.5 and 4 minutes, inclusive. 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. a. . P(x>1.5) ( a. A good example of a discrete uniform distribution would be the possible outcomes of rolling a 6-sided die. The Standard deviation is 4.3 minutes. 11 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. 23 The sample mean = 7.9 and the sample standard deviation = 4.33. Use the following information to answer the next three exercises. Required fields are marked *. (b-a)2 =0.8= 12 15 Let x = the time needed to fix a furnace. All values x are equally likely. In order for a bus to come in the next 15 minutes, that means that it has to come in the last 5 minutes of 10:00-10:20 OR it has to come in the first 10 minutes of 10:20-10:40. \(X\) is continuous. 41.5 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). X is continuous. 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. The age of a first grader on September 1 at Garden Elementary School is uniformly distributed from 5.8 to 6.8 years. What is the . Posted at 09:48h in michael deluise matt leblanc by So, P(x > 12|x > 8) = \(a\) is zero; \(b\) is \(14\); \(X \sim U (0, 14)\); \(\mu = 7\) passengers; \(\sigma = 4.04\) passengers. The probability a person waits less than 12.5 minutes is 0.8333. b. = Except where otherwise noted, textbooks on this site looks like this: f (x) 1 b-a X a b. The probability of drawing any card from a deck of cards. For this problem, \(\text{A}\) is (\(x > 12\)) and \(\text{B}\) is (\(x > 8\)). Let \(X =\) the time, in minutes, it takes a student to finish a quiz. The graph of the rectangle showing the entire distribution would remain the same. The probability density function of \(X\) is \(f(x) = \frac{1}{b-a}\) for \(a \leq x \leq b\). Sketch the graph of the probability distribution. Find the probability that the truck drivers goes between 400 and 650 miles in a day. \(k = 2.25\) , obtained by adding 1.5 to both sides. The distribution is ______________ (name of distribution). 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. Shade the area of interest. A fireworks show is designed so that the time between fireworks is between one and five seconds, and follows a uniform distribution. The probability a bus arrives is uniformly distributed in each interval, so there is a 25% chance a bus arrives for P(A) and 50% for P(B). 1.5+4 15+0 Would it be P(A) +P(B) + P(C) - P(A and B) - P(A and C) - P(B and C) - P(A and B and C)? b. 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. The waiting time for a bus has a uniform distribution between 0 and 10 minutes. 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The cumulative distribution function of X is P(X x) = \(\frac{x-a}{b-a}\). What does this mean? Thus, the value is 25 2.25 = 22.75. What is P(2 < x < 18)? 23 \(0.75 = k 1.5\), obtained by dividing both sides by 0.4 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 . \(P(2 < x < 18) = 0.8\); 90th percentile \(= 18\). The data follow a uniform distribution where all values between and including zero and 14 are equally likely. Let X = the time, in minutes, it takes a nine-year old child to eat a donut. What is the probability that a bus will come in the first 10 minutes given that it comes in the last 15 minutes (i.e. Note that the length of the base of the rectangle . Let X= the number of minutes a person must wait for a bus. The lower value of interest is 0 minutes and the upper value of interest is 8 minutes. 1 This means that any smiling time from zero to and including 23 seconds is equally likely. Example The data in the table below are 55 smiling times, in seconds, of an eight-week-old baby. Let X = the time needed to change the oil on a car. However, the extreme high charging power of EVs at XFC stations may severely impact distribution networks. Let X = length, in seconds, of an eight-week-old baby's smile. Find the probability that she is between four and six years old. In real life, analysts use the uniform distribution to model the following outcomes because they are uniformly distributed: Rolling dice and coin tosses. Random sampling because that method depends on population members having equal chances. Find the probability that a randomly selected furnace repair requires more than two hours. McDougall, John A. The longest 25% of furnace repairs take at least 3.375 hours (3.375 hours or longer). for 0 x 15. P(x>12ANDx>8) Sketch the graph, shade the area of interest. The data that follow are the square footage (in 1,000 feet squared) of 28 homes. A distribution is given as X ~ U(0, 12). P(x>8) a+b 23 Extreme fast charging (XFC) for electric vehicles (EVs) has emerged recently because of the short charging period. a. 2 12 b is 12, and it represents the highest value of x. This means you will have to find the value such that \(\frac{3}{4}\), or 75%, of the cars are at most (less than or equal to) that age. a. = Formulas for the theoretical mean and standard deviation are, = P(x>8) 1 The longest 25% of furnace repairs take at least 3.375 hours (3.375 hours or longer). Beta distribution is a well-known and widely used distribution for modeling and analyzing lifetime data, due to its interesting characteristics. There are two types of uniform distributions: discrete and continuous. 12 3.5 This distribution is closed under scaling and exponentiation, and has reflection symmetry property . What are the constraints for the values of \(x\)? 0.90 . 3.5 It would not be described as uniform probability. The total duration of baseball games in the major league in the 2011 season is uniformly distributed between 447 hours and 521 hours inclusive. a. 1 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). \(P(x > k) = 0.25\) 12 \(\sigma = \sqrt{\frac{(b-a)^{2}}{12}} = \sqrt{\frac{(12-0)^{2}}{12}} = 4.3\). admirals club military not in uniform. We write \(X \sim U(a, b)\). A distribution is given as \(X \sim U(0, 20)\). If a random variable X follows a uniform distribution, then the probability that X takes on a value between x1 and x2 can be found by the following formula: For example, suppose the weight of dolphins is uniformly distributed between 100 pounds and 150 pounds. \(0.25 = (4 k)(0.4)\); Solve for \(k\): Find the probability that the commuter waits less than one minute. 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 time follows a uniform distribution. 3.375 = k, We write X U(a, b). Sketch the graph, and shade the area of interest. The waiting times for the train are known to follow a uniform distribution. Sixty percent of commuters wait more than how long for the train? c. This probability question is a conditional. obtained by dividing both sides by 0.4 a. Lowest value for \(\overline{x}\): _______, Highest value for \(\overline{x}\): _______. a= 0 and b= 15. P(x>8) 15 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. OpenStax is part of Rice University, which is a 501(c)(3) nonprofit. a+b 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. It is assumed that the waiting time for a particular individual is a random variable with a continuous uniform distribution. Let \(k =\) the 90th percentile. Is this because of the multiple intervals (10-10:20, 10:20-10:40, etc)? Suppose the time it takes a nine-year old to eat a donut is between 0.5 and 4 minutes, inclusive. The total duration of baseball games in the major league in the 2011 season is uniformly distributed between 447 hours and 521 hours inclusive. You must reduce the sample space. 5 (b-a)2 What has changed in the previous two problems that made the solutions different. 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. You already know the baby smiled more than eight seconds. 12 )=0.90, k=( a+b The probability density function is Note: We can use the Uniform Distribution Calculator to check our answers for each of these problems. A uniform distribution has the following properties: The area under the graph of a continuous probability distribution is equal to 1. Solution Let X denote the waiting time at a bust stop. The probability density function of X is \(f\left(x\right)=\frac{1}{b-a}\) for a x b. The longest 25% of furnace repairs take at least 3.375 hours (3.375 hours or longer). P(AANDB) The cumulative distribution function of \(X\) is \(P(X \leq x) = \frac{x-a}{b-a}\). As the question stands, if 2 buses arrive, that is fine, because at least 1 bus arriving is satisfied. It explains how to. Write the probability density function. On the average, how long must a person wait? Find the probability that a person is born after week 40. = For example, if you stand on a street corner and start to randomly hand a $100 bill to any lucky person who walks by, then every passerby would have an equal chance of being handed the money. The notation for the uniform distribution is. 23 15 A continuous random variable X has a uniform distribution, denoted U ( a, b), if its probability density function is: f ( x) = 1 b a. for two constants a and b, such that a < x < b. a. 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 answer for 1) is 5/8 and 2) is 1/3. The probability a person waits less than 12.5 minutes is 0.8333. b. The data in [link] are 55 smiling times, in seconds, of an eight-week-old baby. 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