For each of the following examples, decide whether x is a binomial random variable and explain your decision:

a. A student is answering 25 multiple choices questions in which each question is accompanied by four answer choices. Let x represent the number of questions that the student answers correctly.

b. A teacher has to select two students to represent the class in an international public speaking competition. Five students have applied to join and appear to be equally qualified for the competition, but in fact only 3 have passed the final selection round (the results of the final selection round have not reached the teacher yet). Suppose the teacher selects two students at random from the five students. Let x be the number of students who passed the final selection round selected.

c. A receptionist at an office receives calls at the front desk daily. Let x represent the number of calls she receives on a specified workday.

d. A medical center claims that about one out of every 50 children in the world may develop a new disease. Suppose you consider a group of 500 children in your study to test the veracity of the claim. Let x be the number of children in your sample who get the new disease.