Probability, Random Variables, and Probability Distributions

If the probability that an individual randomly selected from a population prefers brand A over brand B is 0.3, and you select 150 individuals at random, which of the following is the approximate standard deviation of the number of individuals who prefer brand A?

If the probability of success on a single trial in a binomial experiment is 0.2 and we want to find the probability of exactly three successes in ten trials, which calculation is appropriate?

If you were told that only six out of twenty sampled marbles drawn at random are blue and assuming these draws represent Bernoulli trials, what information would you still require to determine if this forms part of data appropriately modeled by the binomial distribution?

When increasing the number of trials in a binomial experiment, what is the effect on the shape of the distribution if p remains constant?

What is the maximum likelihood estimator (MLE) for the parameter p in a binomial distribution where k=800 successes were observed over 4000 trials?

How is cluster-sampling different than stratified-sampling?

Which term describes the probability of success on an individual trial in a binomial distribution?

When flipping a fair coin three times, what parameter represents the expected number of tails?

How does increasing only the probability of success ('p') while keeping the number of trials ('n') constant affect the standard deviation of a binomial distribution?

What is the probability of success in a binomial distribution called?