Determine whether or not the random variable X is a binomial random variable. If so, give the values of n and p. If not, explain why not. a. X is the number of dots on the top face of fair die that is rolled. b. X is the number of defective parts in a sample of ten randomly selected parts coming from a manufacturing process in which 0.02% of all parts are defective.

Answer:Both are binomials.Step-by-step explanation:Given that a) X is the number of dots on the top face of fair die that is rolled. When a fair die is rolled, there will be 1 to 6 numbers on each side with dots in that.  Each time a die is rolled the events are independent.  Hence probability of getting a particular number in the die is 1/6. There will be two outcomes either the number or not the number.  Hence X no of times we get a particular number of dots on the top face of fair die that is rolled is binomial with n = no of rolls, and p = 1/6b) X is the number of defective parts in a sample of ten randomly selected parts coming from a manufacturing process in which 0.02% of all parts are defective.Here X has two outcomes whether defective or non defective.  EAch part is independent of the other in the sense that the probability for each trial is constant with 0.02% =p and no of trials = n = 10.