Question: Suppose that a simple random sample of 200 is taken from the shipment of 10,000 electronic components of Exercise 15, which contais 300 defective components, and let Y denote the number of defective components in the sample.
(a) The random variable Y has a hypergeometric(M1, M2, n) distribution, which can be approximated by a binomial(n, p) distribution, which can be approximated by a Poisson(λ) distribution. Specify the parameters of each distribution mentioned in the last sentence.
(b) Use R commands to compute the exact probability P(Y ≤ 10), as well as the two approximations to this probability mentioned in part (a).
Exercise 15
In a shipment of 10,000 of a certain type of electronic component, 300 are defective. Suppose that 50 components are selected at random for inspection, and let X denote the number of defective components found.
(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(X ≤ 3).
(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(X ≤ 3), and compare it with the exact probability found in part (b).