Binomial Distribution

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Show your work for each problem.

1.
Which of the following is a condition for a binomial distribution?
1. a)Each trial must be independent
2. b)The number of trials is unlimited
3. c)Each trial must have at least 3 outcomes
4. d)The probability changes after each trial
2.
Calculate . Enter your answer as a number.
3.
In the binomial formula , what does represent?
1. a)The number of failures
2. b)The variance
3. c)The probability of failure on each trial
4. d)The expected value
4.
You flip a fair coin 4 times. What is the probability of getting exactly 2 heads?
5.
If and , what is the mean of the binomial distribution?
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?
1. a)
2. b)
3. c)
4. d)
7.
A factory produces items with a 5% defect rate. What is the probability that exactly 1 out of 10 items is defective?
8.
Calculate the standard deviation for a binomial distribution with and . Round to 2 decimal places.
9.
Which of the following is NOT a binomial experiment?
1. a)Rolling a die and checking if it shows 6
2. b)Testing if 20 light bulbs work or fail
3. c)Drawing cards without replacement
4. d)Flipping a coin 10 times
10.
A vaccine is 80% effective. If 6 people are vaccinated, what is the probability that exactly 5 develop immunity?
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.
A drug has a 70% success rate. If 8 patients are treated, what is the probability that at least 7 respond positively?
13.
For which value of does a binomial distribution have the largest variance when ?
1. a)
2. b)
3. c)
4. d)
14.
If for a binomial distribution with , what is ? Round to 1 decimal place.
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.
A fair die is rolled 12 times. What is the expected number of sixes?
1. a)6
2. b)2
3. c)1
4. d)12
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?