Question: An engineer at a construction firm has a subcontract for the electrical work in the construction of a new office building. From past experience with this electrical subcontractor, the engineer knows that each light switch that is installed will be faulty with probability p = 0.002 independent of the other switches installed. The building will have n = 1500 light switches in it. Let X be the number of faulty light switches in the building.
(a) The distribution of the random variable X is (choose one)
(i) binomial
(ii) hypergeometric
(iii) negative binomial
(iv) Poisson.
(b) Use R commands to find P(4 ≤ X ≤ 8).
(c) Which distribution from those listed in part (a) can be used as an approximation to the distribution of X?
(d) Using the approximate distribution, give an approximation to the probability P(4 ≤ X ≤ 8), and compare it with the exact probability found in part (b).
(e) Compute the exact and approximate probability of no faulty switches.