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- Find the value of k for the probability mass function 4 f(x) = k () , ) for x = 0,1,2. %3| 4 -Defects occur along the length of cable at an average of 5 defects per 4,000 feet. Assume that the probability of k defects int feet of cable is given by the probability mass function: e -(5t/ 4000) ( 5 t/ 4,000 ) k P(k defects ) = k ! for k = 0, 1, 2, .. Find the probability that a .... 3,200 foot cable will have а. at most three defects b. at least four defects С. between 1 to 5 (inclusive) defectsWhile taking a walk along the road where you live, you accidentally drop your glove, but you don't know where. The probability density p(x) for having dropped the glove a kilometers from home (along the road) is p(x) = 2e-2 for x ≥ 0 a. What is the probability that you dropped it within 1 kilometer of home? I b. At what distance y from home is the probability that you dropped it within y km of home equal to 0.95? km <-|
- The bearing capacity of the soil under a foundation is measured to range from 200 kPA to 450 kPA. The probability density within this range is given by engineering office as f(x) = 3 ,200< x < 450 450 ,otherwise If you know that the column on which stands is designed to carry a load 275 kPA, what is the probability of the failure of the foundation? Do you think redesigning project is necessary?A company uses wood chips in the manufacture of processed wood pieces of various sizes. Suppose the tons of wood chips T used per day has a probability density function f(T) = 0.25e-0.25T (a) Find the probability of using more than 4 tons of wood chips in a day. (Round your answer to three decimal places.) (b) Find the number of tons 7 (to the nearest ton) so that the probability of using more than 7 tons in a day is 0.07. tonsansewr D and E only
