Binomial Distribution

Practice Problems: Binomial Distribution

1. 1. Which of the following is a condition for a binomial distribution?
2. 2. Calculate $\binom{6}{2}$. Enter your answer as a number.
3. 3. In the binomial formula $P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$, what does $(1-p)$ represent?
4. 4. You flip a fair coin 4 times. What is the probability of getting exactly 2 heads?
5. 5. If $n = 10$ and $p = 0.3$, what is the mean $\mu$ of the binomial distribution?
6. 6. A basketball player has a 60% free throw success rate. If she takes 5 shots, what expression gives the probability of making exactly 3?
7. 7. A factory produces items with a 5% defect rate. What is the probability that exactly 1 out of 10 items is defective?
8. 8. Calculate the standard deviation for a binomial distribution with $n=20$ and $p=0.5$. Round to 2 decimal places.
9. 9. Which of the following is NOT a binomial experiment?
10. 10. A vaccine is 80% effective. If 6 people are vaccinated, what is the probability that exactly 5 develop immunity?
11. 11. A test has 8 multiple choice questions with 4 options each. If a student guesses randomly, what is the probability of getting exactly 2 correct? Round to 3 decimal places.
12. 12. A drug has a 70% success rate. If 8 patients are treated, what is the probability that at least 7 respond positively?
13. 13. For which value of $p$ does a binomial distribution have the largest variance when $n=12$?
14. 14. If $P(X=0) = 0.0778$ for a binomial distribution with $n=5$, what is $p$? Round to 1 decimal place.
15. 15. A company knows 20% of its emails are spam. If 10 emails arrive, what is the probability of receiving at most 1 spam email?
16. 16. A fair die is rolled 12 times. What is the expected number of sixes?
17. 17. In a survey, 40% of people prefer tea over coffee. If 7 people are randomly selected, what is the probability that exactly 4 prefer tea?