Question 5:'Time headway' in traffic flow is the elapsed time between the time that one car finishes passing afixed point and the instant that the next car begins to pass that point. Let X be the time headway for two randomly chosenconsecutive cars (in seconds). Suppose X has pdff(x)=Ja> 1To x ≤ 1(a) Find the value of k.(b) Obtain the mean value of headway and the standard deviation of headway.(c) The cdf of X isF(x) ={:.x ≤ 11- x>1Using the cdf, determine the following probabilities.(i) What is the probability that observed depth is at most 3?(ii) What is the probability that observed depth is between 3 and 2?

Answered: Image /qna-images/answer/d8ff8570-a55f-437f-bffd-ae8c09b325fc.jpg

Answered: 10 x≤1 (a) Find the value of k. (b)…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Scores for students on the verbal portion of the SAT-I test are normally distributed with a mean of 509 and a standard deviation of 108. A random sample of 36 students who took the SAT-I test is selected. Let ?̅ represent the mean score of the sample. 4. The probability that the sample mean score ?̅ is greater than 540 is about (a) 0.9573 (b) 0.5427 (c) 0.6554 (d) 0.0427 (e) 0.17
you should calculate the required probabilities using tables A model for normal human body temperature, X, when measured orally in F, is that it is normally distributed, X N(98.2, 0.5184). According to the model that you just derived for W, what proportion of people have a normal body temperature of between 36 °C and 36.8 C? ()
Previous studies have suggested that human body temperature is normally distributed with a mean of 98.6∘98.6∘ F and a standard deviation of 0.7∘0.7∘ F. You sample 75 random humans and find ¯x=97.1∘x¯=97.1∘ F. To estimate the typical human's body temperature,we should use: 2-PropZInt 2-SampZInt 2-SampTInt ZInterval TInterval 1-PropZInt
A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1463 and the standard deviation was 314. The test scores of four students selected at random are 1870, 1220, 2190, and 1340. Find the z-scores ← that correspond to each value and determine whether any of the values are unusual. F1 The z-score for 1870 is (Round to two decimal places as needed.) The z-score for 1220 is. (Round to two decimal places as needed.) The z-score for 2190 is (Round to two decimal places as needed.) The z-score for 1340 is. (Round to two decimal places as needed.) Which values, if any, are unusual? Select the correct choice below and, if necessary, fill in the answer box within your choice. OA. The unusual value(s) is/are. (Use a comma to separate answers as needed.) OB. None of the values are unusual. F2 80 F3 000 000 F4 F5 ^ MacBook Air F6 & A D F7 * DII F8 DD F9 ) J 운 F10 I a F11 + Next F12 delete
Let x denote the time taken to run a road race. Suppose x is approximately normally distributed with a mean of 190 minutes and a standard deviation of 21 minutes. If one runner is selected at random, what is the probability that this runner will complete this road race in 224 to 236 minutes? Round your answer to four decimal places. i
The weekly demand for Papa Chubby’s pizzas on a Friday night is a randomvariable with mean 230 and standard deviation 10. Find the value(s) of X for eachevent. Show your work.(1) Lowest 50 percent(2) Highest 25 percent(3) 90th percentile(4) Middle 80 percent
The percent of fat calories that a person consumes each day is normally distributed with a mean of about 35 and a standard deviation of about ten. Suppose that 9 individuals are randomly chosen. Let X = average percent of fat calories. For the group of 9, find the probability that the average percent of fat calories consumed is more than six. (Round your answer to four decimal places.)
***Only do this question if using Minitab and show images*** Let X1, X2, X3, . . . , X200 denote the weights of 200 independent and identically distributed bags of candy corn. If the mean weight of each bag is 2 lb. and its standard deviation is 0.07 lb., determine the probability that the average of 200 bags weighs between 1.997 lb. and 2.06 lb. Show your answer using Minitab.
A pizza company advertises that it puts 0.5 pounds of real mozzarella cheese on its medium pizzas. Suppose that the amount of cheese on a randomly selected medium pizza is normally distributed with a mean value of 0.5 pounds and a standard deviation of 0.005 pounds. (Let y = the amount of cheese on a medium pizza. Round the answers to three decimal places.) (a) What is the probability that the amount of cheese on a medium pizza is between 0.505 and 0.510 pounds?P(0.505 ≤ y ≤ 0.510) = (b) What is the probability that the amount of cheese on a medium pizza exceeds the mean value by more than 2 standard deviations?P(y > ? + 2?) = (c) What is the probability that four randomly selected medium pizzas all have at least 0.495 pounds of cheese?
+ I/ * 00 A company manufactures light bulbs. The company wants the bulbs to have a mean life span of 997 hours. This average is maintained by periodically testing random samples of 16 light bulbs. If the t-value falls between -th an and t, go then the company will be satisfied that it is manufacturing acceptable light bulbs. For a random sample, the mean life span of the sample is 1002 hours and the standard deviation is 29 hours. Assume that life spans are approximately normally distributed. Is the company making acceptable light bulbs? Explain. and to 90 The company making acceptable light bulbs because the t-value for the sample is t= (Round to two decimal places as needed.) Get more help- Clear all Check answer 3:44 PM 64°F Sunny A 11/23/2021 PrtSc F5. F10 F11 F12 4. 5. 9. 6. K. B. M.
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