For each scenario described, state whether or not the binomial distribution is a reasonable model for the random variable and why. State any assumptions you make.
(a) A production process produces thousands of temperature transducers. Let X denote the number of nonconforming transducers in a sample of size 30 selected at random from the process.
(b) From a batch of 50 temperature transducers, a sample of size 30 is selected without replacement. Let X denote the number of nonconforming transducers in the sample.
(c) Four identical electronic components are wired to a controller. Let X denote the number of components that have failed after a specified period of operation.
(d) Let X denote the number of express mail packages received by the post office in a 24-hour period.
(e) Let X denote the number of correct answers by a student taking a multiple choice exam in which a student can eliminate some of the choices as being incorrect in some questions and all of the incorrect choices in other questions.
(f) Forty randomly selected semiconductor chips are tested. Let X denote the number of chips in which the test finds at least one contamination particle.
(g) Let X denote the number of contamination particles found on 40 randomly selected semiconductor chips.
(i) Errors in a digital communication channel occur in bursts that affect several consecutive bits. Let X denote the number of bits in error in a transmission of 100,000 bits.
(j) Let X denote the number of surface flaws in a large coil of galvanized steel.