c) The number of flaws in a new brand of fibre optic cable is known to follow a Poisson distribution, with a mean of 2 flaws per 100 metres of cable. i. Use the output below to determine the probability of observing 5 flaws in 100 metres of cable, i.e. P(X = 5) dpois (5, lambda = 100) [1] 3.100063e-36 dpois (5, lambda = 2) [1] 0.03608941 dpois (2, lambda = 5) [1] 0.08422434 dpois (100, lambda = 5) [1] 5.695402e-91 ii. Use the output below to determine the probability of at least 3 flaws in 100 metres of cable, i.e. P(X > 3) sum (dpois (0:2, lambda = 2)) %3D [1] 0.6766764 1-sum (dpois (0:2, lambda = 2)) [1] 0.3233236 sum (dpois (0:2, lambda = 3)) [1] 0.4231901 1-sum (dpois (0:2, lambda = 3)) [1] 0.5768099

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