4. The time required in the first step of a manufacturing process is a normally-distributed random variable with mean = 45 min and standard deviation = 4 min. The time required in the second step of the manufacturing process is also a normally-distributed random variable with mean = 24 min and standard deviation = 3 min. a) What is the probability that the time required to complete both of those steps will be greater than 75 min? b) What is the probability that the time required to complete both steps will be no more than 70 min?
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- Two components are being considered for use in building a system in your manufacturing plant. The lifetime of component 1 is modeled by a normal random variable with mean 20,000 hours and standard deviation of 5000 hours (ignore the fact the this model can technically give negative values for lifetime - that probability is practically zero). The lifetime of component 2 is also a normal random variable but with mean 22,000 hours and standard deviation 1000 hours. Which component has the highest probability of functioning for the life of the system if the target lifetime is 20,000 hours? What about a target lifetime of 24,000 hours?The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.4 minutes and a standard deviation of 3.3 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. (a) What is the probability that for 38 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)(b) What is the probability that for 38 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)(c) What is the probability that for 38 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)The time needed to complete a final examination in a particular college course is normally distributed with a mean of 160 minutes and a standard deviation of 25 minutes. Answer the following questions: a) What is the probability of completing the exam in 120 minutes or less? b) What is the probability that a student will complete the exam in more than 120 minutes but less than 150 minutes? c) What is the probability that a student will complete the exam in more than 100 minutes but less than 170 minutes? d) Assume that the class has 120 students and that the examination period is 180 minutes in length. How many students do you expect will not complete the examination in the allotted time?
- The number of clients arriving at a bank machine is Poisson distributed with an average of 2 per minute. For a 5-minute period, Find the expected value and standard deviation. What is the probability that 2 customers will arrive in a 5-minute period? What is the probability that no more than 2 customers will arrive in a 5-minute period? What are the underlying assumptions that allow us to consider this phenomenon as a Poisson distribution?Assume that the square footage of a residential house in the US is normally distributed with a mean=1000 and standard deviation=150 square feet. If we select a random house what is the probability that it will be at most 1050 square feet?The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.6 minutes and a standard deviation of 3 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. (a) What is the probability that for 35 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)(b) What is the probability that for 35 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)(c) What is the probability that for 35 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)
- The taxi and takeoff time for commercial jets is a random variable x with a mean of 9 minutes and a standard deviation of 3.4 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. (a) What is the probability that for 35 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.) (b) What is the probability that for 35 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.) (c) What is the probability that for 35 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.) US 12:44 hp DII -> & $ @ 7 8 3. 4 5 i y r W k d m V .. ..The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.5 minutes and a standard deviation of 3.2 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. (a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.) (b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.) (c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)5
- A factory's worker productivity is normally distributed. One worker produces an average of 73 units per day with a standard deviation of 19. Another worker produces at an average rate of 66 units per day with a standard deviation of 20. A. What is the probability that in a single day worker 1 will outproduce worker 2? Probability= B. What is the probability that during one week (5 working days), worker 1 will outproduce worker 2? Probability =9) The probability that a 2011 Audi A8 will be stolen is .0048. Find the odds against the theft of a 2011 Audi A8. Round your answer to the nearest whole number. Odds against a 2011 Audi being stolen is to 10) The probability that an international flight leaving the United States is delayed in departing (event D) is .35. The probability that an international flight leaving the United States is a transpacific flight (event P) is .40. The probability that an international flight leaving the U.S. is a transpacific flight and is delayed in departing is .14. (a) What is the probability that an international flight leaving the United States is delayed in departing given that the flight is a transpacific flight? (Round your answer to 4 decimal places.) Probability (b) In this problem, are D and P independent? No Yes 11) The fracture strength of a certain type of manufactured glass is normally distributed with a mean of 579 MPa with a standard deviation of 14 MPa. (a) What is the probability…The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.2 minutes and a standard deviation of 3.2 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. (a) What is the probability that for 36 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)(b) What is the probability that for 36 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)(c) What is the probability that for 36 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)