Answer:
(a) The probability of exactly three flaws in 150 m of cable is 0.21246
(b) The probability of at least two flaws in 100m of cable is 0.69155
(c) The probability of exactly one flaw in the first 50 m of cable, and exactly one flaw in the second 50 m of cable is 0.13063
Step-by-step explanation:
A random variable X has a Poisson distribution and it is referred to as Poisson random variable if and only if its probability distribution is given by
for x = 0, 1, 2, ...
where , the mean number of successes.
(a) To find the probability of exactly three flaws in 150 m of cable, we first need to find the mean number of flaws in 150 m, we know that the mean number of flaws in 50 m of cable is 1.2, so the mean number of flaws in 150 m of cable is
The probability of exactly three flaws in 150 m of cable is
(b) The probability of at least two flaws in 100m of cable is,
we know that the mean number of flaws in 50 m of cable is 1.2, so the mean number of flaws in 100 m of cable is
(c) The probability of exactly one flaw in the first 50 m of cable, and exactly one flaw in the second 50 m of cable is
The occurrence of flaws in the first and second 50 m of cable are independent events. Therefore the probability of exactly one flaw in the first 50 m and exactly one flaw in the second 50 m is