Homework 1: l. A mechanical system with 5 pump assemblies will operate satisfact
ID: 3202723 • Letter: H
Question
Homework 1: l. A mechanical system with 5 pump assemblies will operate satisfactorily if any three out of five pumps are functioning. Given that 15% of the total pump production is defective, what is the probability of system malfunction? 2. Past data indicated that there were on an average 4 accidents on a highway per year. Number of accidents per year may be assumed to have Poisson distribution. The mean of Poisson distribution, is given by e. Find the probability of 1) no accidents; 2) 4 accidents, 3) at least 4 accidents per year. 3. A light bulb he lifetime is assumed to follow an exponential distribution) has a mean life of 400 hours. What is the probability of the bulb lasting 1) less than 300 hours; 2) more than 500 hours; 3) between 200 and 500 hours? 4. The acceptable tolerance on a shaft product is 9 t 0.005 in. From past experience, it is known that G 0.003 in. What is the percentage of scrap parts? 5. Determine the normal population that lies within t 1.0o, t 2.0G. t 3.00, t 4.0o.Explanation / Answer
2 Assuming poisson distribution
Given that u = 4 ,
P(x; ) = (e-) (x) / x!
where x is the actual number of successes that result from the experiment, and e is approximately equal to 2.71828.
putting the values in the above equation
for x = 0 , no accidents , u = 4
(e-4) (40) / 0! so the answer is 0.0183
b) In this case , put x = 4 , rest of the values would remain the same so te formula becomes
e-4) (44) / 4! = 0.195
c) for atleast 4 accidents we shall calculate for 0 ,1,2,3 and then substract the final value from 1 (as sum of probabilties can be 1 )
1 - [(e-4) (40) / 0! + (e-4) (41) / 1! + (e-4) (42) / 2! + (e-4) (43) / 3!]
solving this we get
= 0.3711
kindly note that we can only answer 1 full question at a time
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