For each of the following questions, say whether the random process is reasonably a binomial process or not, and explain your answer. If it is not a binomial process, explain what assumptions are not well met. If it is a binomial process, comment on the validity of each of things that must be true for a process to be a binomial process (ex: identify n: the number of Bernoulli trials, # the probability of success, etc).
a. A fair die is rolled until a 1 appears, and X denotes the number of rolls.
b. Twenty of the different Badger basketball players each attempt 1 free throw and X is the total number of successful attempts.
c. A die is rolled 50 times. Let X be the face that lands up.
d. In a bag of 10 batteries, I know 2 are old. Let X be the number of old batteries I choose when taking a sample of 4 to put into my calculator.
e. It is reported that 20% of Madison homeowners have installed a home security system. Let X be the number of homes without home security systems installed in a random sample of 100 houses in the Madison city limits.