5. Binomial Distribution & Discrete Random Variables

In a binomial distribution, how does increasing the value of $n$ (the number of trials) affect the shape of the binomial probability histogram?

Which of the following statements is true for both the binomial and Poisson distributions?

In a binomial experiment, how many possible outcomes are there for a single trial?

Which of the following is a criterion for a binomial probability experiment?

Which of the following is not a requirement of the binomial probability distribution?

Which statement is not true for a binomial distribution with $n=15$ and $p=\frac{1}{20}$?

Suppose a binomial experiment consists of $n$ independent trials, each with probability of success $p$. Which of the following expressions gives the probability of observing exactly $k$ successes?

Which of the following is not a requirement of the binomial probability distribution?

Which of the following is not a requirement of the binomial probability distribution?

Assume that a procedure yields a $binomial$ distribution. Which of the following is a necessary condition for the $binomial$ distribution to apply?

In a binomial experiment with $4$ trials and probability of success $p=0.4$, what is the probability of obtaining exactly $3$ successes?

For a binomial distribution with probability of success $p=\frac{1}{4}$ and number of trials $n=36$, what is the expected value of the distribution?

Which of the following is a criterion for a binomial probability experiment?

In a binomial experiment with $n=20$ trials and probability of success $p=0.70$, what is the expected value (mean) of the number of successes?

A biologist is monitoring a large bird sanctuary where a particular bird species is known to have a 70% success rate for each nesting attempt (at least one chick fledges from the nest). This season, she observes 500 independent nesting attempts across the sanctuary.

(D) What is the probability that 330 – 370 nesting attempts are successful?