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. = 7.5. Let X = the time needed to change the oil on a car. Let x = the time needed to fix a furnace. The longest 25% of furnace repairs take at least 3.375 hours (3.375 hours or longer). Find the 90th percentile for an eight-week-old baby's smiling time. a. 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However, the extreme high charging power of EVs at XFC stations may severely impact distribution networks. FHWA proposes to delete the second and third sentences of existing Option P14 regarding the color of the bus symbol and the use of . You already know the baby smiled more than eight seconds. State this in a probability question, similarly to parts g and h, draw the picture, and find the probability. ba 1 Find P(x > 12|x > 8) There are two ways to do the problem. The sample mean = 2.50 and the sample standard deviation = 0.8302. The standard deviation of \(X\) is \(\sigma = \sqrt{\frac{(b-a)^{2}}{12}}\). Find the third quartile of ages of cars in the lot. What is the 90th percentile of this distribution? f(x) = \(\frac{1}{4-1.5}\) = \(\frac{2}{5}\) for 1.5 x 4. Find the probability that the time is between 30 and 40 minutes. 1 X = The age (in years) of cars in the staff parking lot. The amount of time a service technician needs to change the oil in a car is uniformly distributed between 11 and 21 minutes. The waiting times for the train are known to follow a uniform distribution. Want to create or adapt books like this? Question 2: The length of an NBA game is uniformly distributed between 120 and 170 minutes. Use the following information to answer the next eight exercises. OR. Buses run every 30 minutes without fail, hence the next bus will come any time during the next 30 minutes with evenly distributed probability (a uniform distribution). 1 c. Find the 90th percentile. The sample mean = 11.65 and the sample standard deviation = 6.08. The graph of the rectangle showing the entire distribution would remain the same. To keep advancing your career, the additional CFI resources below will be useful: A free, comprehensive best practices guide to advance your financial modeling skills, Get Certified for Business Intelligence (BIDA). Question 3: The weight of a certain species of frog is uniformly distributed between 15 and 25 grams. It means that the value of x is just as likely to be any number between 1.5 and 4.5. The probability a person waits less than 12.5 minutes is 0.8333. b. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo 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. What is the probability density function? The data follow a uniform distribution where all values between and including zero and 14 are equally likely. \(0.3 = (k 1.5) (0.4)\); Solve to find \(k\): P(x>12ANDx>8) Example 5.2 X ~ U(a, b) where a = the lowest value of x and b = the highest value of x. I thought of using uniform distribution methodologies for the 1st part of the question whereby you can do as such Download Citation | On Dec 8, 2022, Mohammed Jubair Meera Hussain and others published IoT based Conveyor belt design for contact less courier service at front desk during pandemic | Find, read . Random sampling because that method depends on population members having equal chances. . a. b. \(X\) = The age (in years) of cars in the staff parking lot. a = smallest X; b = largest X, The standard deviation is \(\sigma =\sqrt{\frac{{\left(b\text{}a\right)}^{2}}{12}}\), Probability density function:\(f\left(x\right)=\frac{1}{b-a}\) for \(a\le X\le b\), 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) = (base)(height) = (d c)\(\left(\frac{1}{b-a}\right)\). ) The 90th percentile is 13.5 minutes. 15.67 B. The data that follow are the number of passengers on 35 different charter fishing boats. Therefore, each time the 6-sided die is thrown, each side has a chance of 1/6. Find the probability that a person is born at the exact moment week 19 starts. 4 What is the probability that a randomly selected NBA game lasts more than 155 minutes? This means that any smiling time from zero to and including 23 seconds is equally likely. The cumulative distribution function of X is P(X x) = \(\frac{x-a}{b-a}\). a+b obtained by subtracting four from both sides: k = 3.375. P(x > 2|x > 1.5) = (base)(new height) = (4 2)\(\left(\frac{2}{5}\right)\)= ? For each probability and percentile problem, draw the picture. . The 90th percentile is 13.5 minutes. 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. This may have affected the waiting passenger distribution on BRT platform space. You must reduce the sample space. A continuous probability distribution is called the uniform distribution and it is related to the events that are equally possible to occur. 2 The probability density function of \(X\) is \(f(x) = \frac{1}{b-a}\) for \(a \leq x \leq b\). \(P(x < 3) = (\text{base})(\text{height}) = (3 1.5)(0.4) = 0.6\). So, P(x > 21|x > 18) = (25 21)\(\left(\frac{1}{7}\right)\) = 4/7. Note that the length of the base of the rectangle . Find the average age of the cars in the lot. They can be said to follow a uniform distribution from one to 53 (spread of 52 weeks). What percentile does this represent? Notice that the theoretical mean and standard deviation are close to the sample mean and standard deviation in this example. P(B) What is the height of \(f(x)\) for the continuous probability distribution? Find the mean, , and the standard deviation, . P(x 12|x > 8 ) There are two to... 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