2 When working out problems that have a uniform distribution, be careful to note if the data are inclusive or exclusive of endpoints. Find the 30th percentile for the waiting times (in minutes). When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive. I'd love to hear an explanation for these answers when you get one, because they don't make any sense to me. The sample mean = 7.9 and the sample standard deviation = 4.33. In this case, each of the six numbers has an equal chance of appearing. What is the probability that a person waits fewer than 12.5 minutes? 1 (ba) In this distribution, outcomes are equally likely. The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. 1.5+4 b. 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 If the waiting time (in minutes) at each stop has a uniform distribution with A = 0 and B = 5, then it can be shown that the total waiting time Y has the pdf f(y) = 1 25 y 0 y < 5 2 5 1 25 y 5 y 10 0 y < 0 or y > 10 \(P(x < 4) =\) _______. The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. Answer: (Round to two decimal places.) Find the probability. 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. a. 1 admirals club military not in uniform Hakkmzda. 15 2 Solution 2: The minimum time is 120 minutes and the maximum time is 170 minutes. =0.8= \(f(x) = \frac{1}{4-1.5} = \frac{2}{5}\) for \(1.5 \leq x \leq 4\). It means that the value of x is just as likely to be any number between 1.5 and 4.5. Another simple example is the probability distribution of a coin being flipped. . The histogram that could be constructed from the sample is an empirical distribution that closely matches the theoretical uniform distribution. The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. Let X = the time, in minutes, it takes a student to finish a quiz. The sample mean = 7.9 and the sample standard deviation = 4.33. It is assumed that the waiting time for a particular individual is a random variable with a continuous uniform distribution. \(0.625 = 4 k\), k Find the 90th percentile for an eight-week-old babys smiling time. The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. Answer: a. View full document See Page 1 1 / 1 point What is the variance?b. 230 a. 12 1). Use the following information to answer the next eleven exercises. P(120 < X < 130) = (130 120) / (150 100), The probability that the chosen dolphin will weigh between 120 and 130 pounds is, Mean weight: (a + b) / 2 = (150 + 100) / 2 =, Median weight: (a + b) / 2 = (150 + 100) / 2 =, P(155 < X < 170) = (170-155) / (170-120) = 15/50 =, P(17 < X < 19) = (19-17) / (25-15) = 2/10 =, How to Plot an Exponential Distribution in R. Your email address will not be published. That is . X ~ U(a, b) where a = the lowest value of x and b = the highest value of x. 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. This may have affected the waiting passenger distribution on BRT platform space. 5 15 d. What is standard deviation of waiting time? Write the probability density function. then you must include on every digital page view the following attribution: Use the information below to generate a citation. In their calculations of the optimal strategy . k = 2.25 , obtained by adding 1.5 to both sides The amount of time a service technician needs to change the oil in a car is uniformly distributed between 11 and 21 minutes. The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. What percentile does this represent? 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. )( Find the average age of the cars in the lot. 2 12 Uniform distribution can be grouped into two categories based on the types of possible outcomes. Here we introduce the concepts, assumptions, and notations related to the congestion model. 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. The McDougall Program for Maximum Weight Loss. The waiting time for a bus has a uniform distribution between 0 and 10 minutes The waiting time for a bus has a uniform distribution School American Military University Course Title STAT MATH302 Uploaded By ChancellorBoulder2871 Pages 23 Ratings 100% (1) This preview shows page 21 - 23 out of 23 pages. the 1st and 3rd buses will arrive in the same 5-minute period)? The sample mean = 7.9 and the sample standard deviation = 4.33. Solution 1: The minimum amount of time youd have to wait is 0 minutes and the maximum amount is 20 minutes. (41.5) The notation for the uniform distribution is. 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. Note that the shaded area starts at x = 1.5 rather than at x = 0; since X ~ U (1.5, 4), x can not be less than 1.5. A subway train on the Red Line arrives every eight minutes during rush hour. ) A bus arrives at a bus stop every 7 minutes. What is the probability density function? Find the probability. Your starting point is 1.5 minutes. 1 (230) We recommend using a The concept of uniform distribution, as well as the random variables it describes, form the foundation of statistical analysis and probability theory. Shade the area of interest. b is 12, and it represents the highest value of x. Find the probability that the value of the stock is more than 19. That is X U ( 1, 12). Example 5.2 5 P(x>12ANDx>8) hours and \(\sigma =\sqrt{\frac{{\left(41.5\right)}^{2}}{12}}=0.7217\) hours. Let \(X =\) the time, in minutes, it takes a student to finish a quiz. If we create a density plot to visualize the uniform distribution, it would look like the following plot: Every value between the lower bounda and upper boundb is equally likely to occur and any value outside of those bounds has a probability of zero. The 30th percentile of repair times is 2.25 hours. b. State the values of a and b. Jun 23, 2022 OpenStax. Then \(X \sim U(0.5, 4)\). b. 41.5 We randomly select one first grader from the class. Notice that the theoretical mean and standard deviation are close to the sample mean and standard deviation in this example. Find the probability that a randomly chosen car in the lot was less than four years old. 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). The unshaded rectangle below with area 1 depicts this. The graph illustrates the new sample space. a. \(P\left(x 12|x > 8) = \frac{(x > 12 \text{ AND } x > 8)}{P(x > 8)} = \frac{P(x > 12)}{P(x > 8)} = \frac{\frac{11}{23}}{\frac{15}{23}} = \frac{11}{15}\). The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. 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. 23 5. 12 The probability that a randomly selected nine-year old child eats a donut in at least two minutes is _______. A good example of a discrete uniform distribution would be the possible outcomes of rolling a 6-sided die. 15 15 = 23 Not sure how to approach this problem. Let k = the 90th percentile. Can you take it from here? (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.) k All values \(x\) are equally likely. (b) The probability that the rider waits 8 minutes or less. (ba) c. This probability question is a conditional. a. It is generally represented by u (x,y). 2 15+0 Find \(a\) and \(b\) and describe what they represent. For this example, \(X \sim U(0, 23)\) and \(f(x) = \frac{1}{23-0}\) for \(0 \leq X \leq 23\). 1 230 0.90=( (In other words: find the minimum time for the longest 25% of repair times.) You must reduce the sample space. 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. P(x>2ANDx>1.5) a. Find the mean, , and the standard deviation, . b. = \(\frac{a\text{}+\text{}b}{2}\) \(P(x < k) = (\text{base})(\text{height}) = (k 1.5)(0.4)\) When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive. Then X ~ U (6, 15). (a) What is the probability that the individual waits more than 7 minutes? The mean of X is \(\mu =\frac{a+b}{2}\). for a x b. What is the height of \(f(x)\) for the continuous probability distribution? The graph of the rectangle showing the entire distribution would remain the same. Sixty percent of commuters wait more than how long for the train? obtained by subtracting four from both sides: \(k = 3.375\) Would be the possible outcomes it takes a student to finish a quiz eight-week-old babys smiling time = )! Decimal places. in other words: find the 90th percentile for an eight-week-old babys time... 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