5. Binomial Distribution & Discrete Random Variables

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?

In Exercises 21–26, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities

Thirty-six percent of Americans think there is still a need for the practice of changing their clocks for Daylight Savings Time. You randomly select seven Americans. Find the probability that the number who say there is still a need for changing their clocks for Daylight Savings Time is (c) at least six.

For the binomial distribution, which of the following expressions correctly represents the probability of obtaining exactly $k$ successes in $n$ independent trials, each with probability of success $p$?

Consider a binomial experiment with $n=5$ and $p=0.3$. What is the probability that exactly 2 successes occur, that is, compute $P(X=2)$ (to 4 decimals)?

A basketball player normally has a 70% chance of making a free throw. The player shoots until finally making a basket, where $x$ is the number of shots they take. Is this a binomial experiment?

You take a 6-question quiz with True/False questions. What is the probability of getting all 6 questions correct by simply guessing?

National surveys indicate that 36% of people have been in a car accident in the last 5 years. If you randomly sample 10 people, how likely is that exactly 4 have had an accident in the last 5 years?

Based on historical weather data in a certain city, about 62% of the days are cloudy. Find the mean, standard deviation, and variance for the number of cloudy days in a 30-day month.