150 The longest 25% of furnace repair times take at least how long? What is the 90th . The amount of timeuntilthe hardware on AWS EC2 fails (failure). This means that any smiling time from zero to and including 23 seconds is equally likely. Find the probability that a randomly selected student needs at least eight minutes to complete the quiz. 4 b. 1. In reality, of course, a uniform distribution is . When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive of endpoints. 15 = What is the probability that the waiting time for this bus is less than 5.5 minutes on a given day? Pdf of the uniform distribution between 0 and 10 with expected value of 5. Use the following information to answer the next eight exercises. 5 We are interested in the weight loss of a randomly selected individual following the program for one month. The amount of time a service technician needs to change the oil in a car is uniformly distributed between 11 and 21 minutes. The probability is constant since each variable has equal chances of being the outcome. 1 (41.5) It is generally represented by u (x,y). Notice that the theoretical mean and standard deviation are close to the sample mean and standard deviation in this example. X = The age (in years) of cars in the staff parking lot. The probability that a randomly selected nine-year old child eats a donut in at least two minutes is _______. Get started with our course today. a. 15 P(AANDB) b. What is the probability that a randomly selected NBA game lasts more than 155 minutes? In this case, each of the six numbers has an equal chance of appearing. A good example of a continuous uniform distribution is an idealized random number generator. 1 Extreme fast charging (XFC) for electric vehicles (EVs) has emerged recently because of the short charging period. P(x 12|x > 8) = (23 12) 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. There is a correspondence between area and probability, so probabilities can be found by identifying the corresponding areas in the graph using this formula for the area of a rectangle: . k = 2.25 , obtained by adding 1.5 to both sides The sample mean = 7.9 and the sample standard deviation = 4.33. b. Ninety percent of the smiling times fall below the 90th percentile, \(k\), so \(P(x < k) = 0.90\), \[(k0)\left(\frac{1}{23}\right) = 0.90\]. However, there is an infinite number of points that can exist. Draw the graph. citation tool such as. 5.2 The Uniform Distribution. 2 Sketch the graph, and shade the area of interest. for 1.5 x 4. Pandas: Use Groupby to Calculate Mean and Not Ignore NaNs. The data in (Figure) are 55 smiling times, in seconds, of an eight-week-old baby. 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. 2 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. 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. The interval of values for \(x\) is ______. Suppose that the value of a stock varies each day from 16 to 25 with a uniform distribution. Find the 90th percentile. Use the conditional formula, P(x > 2|x > 1.5) = What is the probability density function? = For this example, \(X \sim U(0, 23)\) and \(f(x) = \frac{1}{23-0}\) for \(0 \leq X \leq 23\). 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 \(\frac{4}{5}\). I was originally getting .75 for part 1 but I didn't realize that you had to subtract P(A and B). A distribution is given as X ~ U(0, 12). 23 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. obtained by subtracting four from both sides: k = 3.375 The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. \(a\) is zero; \(b\) is \(14\); \(X \sim U (0, 14)\); \(\mu = 7\) passengers; \(\sigma = 4.04\) passengers. On the average, a person must wait 7.5 minutes. View full document See Page 1 1 / 1 point In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. Let X = the time, in minutes, it takes a nine-year old child to eat a donut. pdf: \(f(x) = \frac{1}{b-a}\) for \(a \leq x \leq b\), standard deviation \(\sigma = \sqrt{\frac{(b-a)^{2}}{12}}\), \(P(c < X < d) = (d c)\left(\frac{1}{b-a}\right)\). 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 data follow a uniform distribution where all values between and including zero and 14 are equally likely. The graph illustrates the new sample space. f(x) = \(\frac{1}{4-1.5}\) = \(\frac{2}{5}\) for 1.5 x 4. Find the 90th percentile for an eight-week-old baby's smiling time. 2 = =45. We will assume that the smiling times, in seconds, follow a uniform distribution between zero and 23 seconds, inclusive. = You can do this two ways: Draw the graph where a is now 18 and b is still 25. 1 P(x>8) For the first way, use the fact that this is a conditional and changes the sample space. \(P(x > k) = 0.25\) P(x>1.5) Suppose that you arrived at the stop at 10:00 and wait until 10:05 without a bus arriving. The total duration of baseball games in the major league in the 2011 season is uniformly distributed between 447 hours and 521 hours inclusive. When working out problems that have a uniform distribution, be careful to note if the data are inclusive or exclusive of endpoints. \(P(2 < x < 18) = 0.8\); 90th percentile \(= 18\). 2 2 Let \(X =\) length, in seconds, of an eight-week-old baby's smile. It is impossible to get a value of 1.3, 4.2, or 5.7 when rolling a fair die. Then X ~ U (0.5, 4). P(x>8) Find the probability that the time is between 30 and 40 minutes. 3.5 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. The Standard deviation is 4.3 minutes. Let x = the time needed to fix a furnace. 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 4 with an area of 0.30 shaded to the left, representing the shortest 30% of repair times. A good example of a discrete uniform distribution would be the possible outcomes of rolling a 6-sided die. So, \(P(x > 12|x > 8) = \frac{(x > 12 \text{ AND } x > 8)}{P(x > 8)} = \frac{P(x > 12)}{P(x > 8)} = \frac{\frac{11}{23}}{\frac{15}{23}} = \frac{11}{15}\). Write the distribution in proper notation, and calculate the theoretical mean and standard deviation. = This is a conditional probability question. For the second way, use the conditional formula from Probability Topics with the original distribution X ~ U (0, 23): P(A|B) = \(\frac{P\left(A\text{AND}B\right)}{P\left(B\right)}\). 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. Find the mean and the standard deviation. a. obtained by subtracting four from both sides: \(k = 3.375\) 41.5 P(x 21|x > 18) = (25 21)\(\left(\frac{1}{7}\right)\) = 4/7. What is P(2 < x < 18)? = The waiting time for a bus has a uniform distribution between 0 and 10 minutes. . . and \(X =\) a real number between \(a\) and \(b\) (in some instances, \(X\) can take on the values \(a\) and \(b\)). Lets suppose that the weight loss is uniformly distributed. a. The notation for the uniform distribution is. (15-0)2 Given that the stock is greater than 18, find the probability that the stock is more than 21. 2.5 P(A and B) should only matter if exactly 1 bus will arrive in that 15 minute interval, as the probability both buses arrives would no longer be acceptable. Let k = the 90th percentile. 238 Statology Study is the ultimate online statistics study guide that helps you study and practice all of the core concepts taught in any elementary statistics course and makes your life so much easier as a student. \(\sigma = \sqrt{\frac{(b-a)^{2}}{12}} = \sqrt{\frac{(12-0)^{2}}{12}} = 4.3\). 2 1 Draw a graph. Births are approximately uniformly distributed between the 52 weeks of the year. The mean of \(X\) is \(\mu = \frac{a+b}{2}\). For this reason, it is important as a reference distribution. X ~ U(a, b) where a = the lowest value of x and b = the highest value of x. If you arrive at the stop at 10:15, how likely are you to have to wait less than 15 minutes for a bus? 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. admirals club military not in uniform. 1 Press question mark to learn the rest of the keyboard shortcuts. Vehicles ( EVs ) has emerged recently because of the short charging period 4.2, or 5.7 when a. Random eight-week-old baby smiles more than 21 as a reference distribution to b is 25. That any smiling time under the Creative Commons Attribution-ShareAlike 4.0 International License than 5.5 minutes on a given day time. 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