Tell whether each of these random variables is binomial; if not, tell which condition is not met (fixed sample size n, independence of selections, just two possible values, and constant probability p of being in the category of interest).
a. Approximately 5% of a school district's 1,000 seniors have no siblings. A random sample of 300 seniors is taken from that district, and X counts the number with no siblings.
b. Approximately 5% of high school seniors have no siblings. A random sample of 300 high school seniors is taken, and X counts the number with no siblings.
c. Approximately 5% of high school seniors have no siblings, 29% have one, 27% have two, and the remaining 39% have three or more. A random sample of 100 high school seniors is taken, and the random variable X counts the number of siblings for each of the sampled seniors.
d. Approximately 5% of high school seniors have no siblings. A survey is taken and X counts the number needed until 20 high school seniors with no siblings have been selected.