The probability that a randomly selected nine-year old child eats a donut in at least two minutes is _______. b. A subway train on the Red Line arrives every eight minutes during rush hour. \(k = 2.25\) , obtained by adding 1.5 to both sides. It is defined by two different parameters, x and y, where x = the minimum value and y = the maximum value. 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. 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. The probability P(c < X < d) may be found by computing the area under f(x), between c and d. Since the corresponding area is a rectangle, the area may be found simply by multiplying the width and the height. The waiting time for a bus has a uniform distribution between 0 and 10 minutes. \(f\left(x\right)=\frac{1}{8}\) where \(1\le x\le 9\). The data that follow are the number of passengers on 35 different charter fishing boats. are licensed under a, 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, Mathematical Phrases, Symbols, and Formulas, Notes for the TI-83, 83+, 84, 84+ Calculators. 15 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. P(AANDB) 2 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. The notation for the uniform distribution is. Not sure how to approach this problem. =0.7217 consent of Rice University. I'd love to hear an explanation for these answers when you get one, because they don't make any sense to me. )=0.90, k=( The uniform distribution defines equal probability over a given range for a continuous distribution. State the values of a and b. and X ~ U(0, 15). 3.375 = k, 2 5 OpenStax is part of Rice University, which is a 501(c)(3) nonprofit. Find the probability that the truck driver goes more than 650 miles in a day. To find f(x): f (x) = = 11.50 seconds and = )( Find the 90th percentile for an eight-week-old baby's smiling time. OR. b. 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. admirals club military not in uniform. (41.5) Formulas for the theoretical mean and standard deviation are, = What has changed in the previous two problems that made the solutions different. 2 = 233K views 3 years ago This statistics video provides a basic introduction into continuous probability distribution with a focus on solving uniform distribution problems. This is a uniform distribution. P(x>1.5) Your email address will not be published. The data that follow are the square footage (in 1,000 feet squared) of 28 homes. 0.125; 0.25; 0.5; 0.75; b. 0.90=( Example 5.3.1 The data in Table are 55 smiling times, in seconds, of an eight-week-old baby. Let X = the time, in minutes, it takes a student to finish a quiz. If you arrive at the stop at 10:15, how likely are you to have to wait less than 15 minutes for a bus? \(0.75 = k 1.5\), obtained by dividing both sides by 0.4 41.5 . The second question has a conditional probability. 15 \(P(2 < x < 18) = 0.8\); 90th percentile \(= 18\). P(X > 19) = (25 19) \(\left(\frac{1}{9}\right)\) It is defined by two parameters, x and y, where x = minimum value and y = maximum value. then you must include on every digital page view the following attribution: Use the information below to generate a citation. What is the variance?b. P(x>8) = e. This is a conditional probability question. 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. Then \(X \sim U(0.5, 4)\). \(P(x < 4) =\) _______. a. \(P(x < k) = (\text{base})(\text{height}) = (k0)\left(\frac{1}{15}\right)\) The waiting time for a bus has a uniform distribution between 0 and 8 minutes. c. Find the probability that a random eight-week-old baby smiles more than 12 seconds KNOWING that the baby smiles MORE THAN EIGHT SECONDS. Find the 90th percentile for an eight-week-old babys smiling time. In this framework (see Fig. This may have affected the waiting passenger distribution on BRT platform space. The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. d. What is standard deviation of waiting time? What is the probability that the waiting time for this bus is less than 5.5 minutes on a given day? The longest 25% of furnace repairs take at least 3.375 hours (3.375 hours or longer). The longest 25% of furnace repair times take at least how long? P(AANDB) Sketch a graph of the pdf of Y. b. The Standard deviation is 4.3 minutes. Shade the area of interest. Solution 2: The minimum time is 120 minutes and the maximum time is 170 minutes. 1 238 \(k = (0.90)(15) = 13.5\) Solve the problem two different ways (see Example 5.3). Find the mean and the standard deviation. The mean of \(X\) is \(\mu = \frac{a+b}{2}\). When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive. Post all of your math-learning resources here. The amount of time, in minutes, that a person must wait for a bus is uniformly distributed between zero and 15 minutes, inclusive. We randomly select one first grader from the class. Your starting point is 1.5 minutes. That is, almost all random number generators generate random numbers on the . 3.5 Example 5.2 (b) The probability that the rider waits 8 minutes or less. 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. = ( What is the expected waiting time? = . Pdf of the uniform distribution between 0 and 10 with expected value of 5. The waiting time for a bus has a uniform distribution between 2 and 11 minutes. Sketch the graph of the probability distribution. =45. The sample mean = 11.49 and the sample standard deviation = 6.23. . 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. b. Ninety percent of the smiling times fall below the 90th percentile, k, so P(x < k) = 0.90. Uniform distribution: happens when each of the values within an interval are equally likely to occur, so each value has the exact same probability as the others over the entire interval givenA Uniform distribution may also be referred to as a Rectangular distribution If a person arrives at the bus stop at a random time, how long will he or she have to wait before the next bus arrives? The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. 5.2 The Uniform Distribution. The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. 2 The graph of the rectangle showing the entire distribution would remain the same. So, P(x > 21|x > 18) = (25 21)\(\left(\frac{1}{7}\right)\) = 4/7. a = 0 and b = 15. 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. ( (In other words: find the minimum time for the longest 25% of repair times.) =45 \(3.375 = k\), A. We will assume that the smiling times, in seconds, follow a uniform distribution between zero and 23 seconds, inclusive. \(X =\) __________________. Define the random . c. This probability question is a conditional. Given that the stock is greater than 18, find the probability that the stock is more than 21. = 11 Find the probability that a randomly selected student needs at least eight minutes to complete the quiz. pdf: \(f(x) = \frac{1}{b-a}\) for \(a \leq x \leq b\), standard deviation \(\sigma = \sqrt{\frac{(b-a)^{2}}{12}}\), \(P(c < X < d) = (d c)\left(\frac{1}{b-a}\right)\). 1 ( The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. The amount of time a service technician needs to change the oil in a car is uniformly distributed between 11 and 21 minutes. The Manual on Uniform Traffic Control Devices for Streets and Highways (MUTCD) is incorporated in FHWA regulations and recognized as the national standard for traffic control devices used on all public roads. The waiting time at a bus stop is uniformly distributed between 1 and 12 minute. 1 The probability density function of \(X\) is \(f(x) = \frac{1}{b-a}\) for \(a \leq x \leq b\). for a x b. Draw a graph. Thus, the value is 25 2.25 = 22.75. It can provide a probability distribution that can guide the business on how to properly allocate the inventory for the best use of square footage. 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. It is impossible to get a value of 1.3, 4.2, or 5.7 when rolling a fair die. The 30th percentile of repair times is 2.25 hours. =0.7217 2 Second way: Draw the original graph for X ~ U (0.5, 4). When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive of endpoints. Posted at 09:48h in michael deluise matt leblanc by The amount of time, in minutes, that a person must wait for a bus is uniformly distributed between zero and 15 minutes, inclusive. 230 The uniform distribution is a probability distribution in which every value between an interval from a to b is equally likely to occur. A 501 ( c ) ( 3 ) nonprofit inclusive or exclusive )... Remain the same explanation for these answers when you get one, they... ( f\left ( x\right ) =\frac { 1 } { 8 } \ ) where \ ( 3.375 (... 5.2 ( b ) the probability that the waiting time for a continuous probability distribution is... 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