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 con- troller. 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 elim- inate some of the choices as being incorrect in some ques- tions and all of the incorrect choices in other questions.