Can you please answer the following MCQ showing any equations and steps? 1-C is
ID: 3131852 • Letter: C
Question
Can you please answer the following MCQ showing any equations and steps?
1-C is a uniform random variable on the interval [ -2k, +8k ]. What is the expected value of C ?
(a) 5k
(b) 10k
(c) 4k
(d) None of the above
2- A local store selling second-hand stereos knows that the lifespan of a second-hand stereo, before it breaks, is uniformly distributed between 0 and 500 days. What is the probability a second-hand stereo lasts less than 110 days ?
(a) 0.78
(b) 0.11
(c) 0.22
(d) None of the above.
3- The time it takes for a freshly laid section of motorway tar to dry is exponentially distributed with a mean of 3.5 hours. What is the probability that it takes a section chosen at random more than 4 hours to dry, correct to two decimal places ?
(a) 0.32
(b) 0.11
(c) 0.68
(d) None of the above.
4- The probability of an engineering student from UCD getting a job overseas within a year of leaving college is 0.12. In a sample of 12 engineers, what is the probability that less than 2 of them will get jobs overseas within a year of leaving college, correct to two decimal places ?
(a) 0.20
(b) 0.57
(c) 0.35
(d) None of the above.
Explanation / Answer
4) probability of getting job oversees = 0.12
probability not getting job oversees = 0.88
we have n = 12
now we have to find p(x<2) = p(0)+p(1)
p(0) = 0.88^12 = 0.215
p(1) = 12C1*(0.12)^1*(0.88)^11 = 0.352
addding both = p(0)+p(1) = 0.215+0.352 = 0.567 = 0.57
hence option b is correct.