please help need it ASAP. if you could give me the formulas to plug in for the answers that would be much appreciated.

Find ux The maintenance department in a factory claims that the number of breakdowns of a particular machine follows a Poisson distribution with a mean of two breakdowns every 500 hours. Let x denote the time in hours) between 2 successive breakdowns. 3 4 Number of breakdowns Per number of hours 5 2 500 6 7 Required: 8 9 Find 10 a) Assuming that the maintenance department's claim is true, find the probability that the time 11 between successive breakdowns is at most five hours. 12 b) Assuming that the maintenance department's claim is true, find the probability that the time 13 between successive breakdowns is between 100 and 300 hours. 14 15 16 17 Students: The scratchpad area is for you to do any additional work you need to solve this question or can be used to show your work. 18 Nothing in this area will be graded, but it will be submitted with your assignment. 19