M Due tomor X Submission X _ BTGE1013 | x Submission X Meet - BTG X Submission X RME_Final X Meet - wza X * Homework X + X C classroom.google.com/c/MzYOMjg10TQ5MzUS S Apps Autodesk Autocad. Reading list BTGE1013 Engineering Mathe Question 4 S 2021/22 a) A factory use predictive maintenance to monitor the performance and condition of operation tools during regular operation to reduce the likelihood of failures. From the analysis, the number of operation tools failures in a day follows a Poisson distribution with an average of 1.25 failures. On a particular day, the stock keeper reported that there were only five replacement tools in stock. A new delivery of replacements tools will only arrive after four days. If all five replacement tools are used before the new delivery arrives, a further replacement cannot be done until the delivery arrives. Upcoming Due today (i) Determine the probability that three replacements of operation tools are required over the next 5:30 AM - SU four days. (5 marks) (ii) Determine the expected number of replacements made over the next four days. (You must show ... all of the details of your calculations) (10 marks) b) From a study which investigates the lifetimes of the LED light bulbs produced by Mr LIGHT are found to be normally distributed with a mean, u of 5500 hours and a standard deviation, o of 120 hours. (i) Determine the probability that a randomly chosen LED light bulb will have a lifetime exceed 5764 hours. (3 marks) (ii) Determine the lifetime by the smallest 0.4% of these LED light bulbs. (2 marks) (iii) From a random sample of 30 LED light bulbs, determine the probability that two out of these 30 LED light bulbs will have a lifetime exceeding 5764 hours. (5 marks) ... 2 [Total: 25 marks] Type here to search C 4:08 AM O 20'C Haze ^ ()8 10/1/2021