Binomial Random Variables

What does the p stand for in the binomial probability formula?

• Number of trials

• Number of Successes

• Probability of Successes

• Probability of Failures

The American College of Obstetricians and Gynecologists reports that 32% of all births in the United States take place by Caesarian section each year. Five woman are about to give birth.

What is the binomial probability that less than 3 will have a C-section birth?

• 0.0391

• 0.1906

• 0.9609

• 0.8095

Answer explanation

Binomial Probability Formula!

n = 5

p = 0.32

q = 1 - p = 0.68

x is "less than 3", so you have to find the probability when x is 2, 1 and 0. Then add them together.

p(0) = 0.1454

p(1) = 0.3421

p(2)=0.322

So, 0.1454 + 0.3421 + 0.322 = 0.8095

Which descriptions are true for a binomial distribution? Select all that apply.

• The probability of success must be the same for each event.

• The probability for each event must be 0.5.

• There can be only two possible outcomes - success and failure.

• The probabilities must add to 1.

• Each trial must be independent.

The American Red Cross says that about 11% of the U.S. population has Type B blood. A blood drive is being held at your school. What is the probability that at least 2 of the first 10 blood donors has Type B blood? 

• 0.088

• 0.697

• 0.214

• 0.303 

Find the mean of the probability distribution.

• 85

• 83.2

• 87.1

• 84.4

Bob is taking a 100 question test.  They have a 90 % probability of getting any one question correct.  WHICH IS THE CORRECT FORMULA TO FIND OUT THE PROBABILITY that they will answer EXACTLY 70  questions correctly?

• ₁₀₀C₇₀   ( 0.18  )³⁰ ( 0.90  )⁷⁰
  

• ₁₀₀C₇₀   ( 0.10  )³⁰ ( 0.90  )⁶⁰

• ₁₀₀C₇₀   ( 0.10  )³⁰ ( 0.90  )⁷⁰

• ₉₉C₇₀   ( 0.10  )³⁰ ( 0.90  )⁷⁰

Suppose that a quiz consists of 20 True-False questions. A student hasn't studied for the exam and will just randomly guesses at all answers (with True and False equally likely). How would you find the probability that the will student get 8 or fewer answers correct?

• Find the probability that X=8 in a binomial distribution with n = 20 and p=0.5.

• Find the area between 0 and 8 in a uniform distribution that goes from 0 to 20.

• Find the probability that X=8 for a normal distribution with mean of 10 and standard deviation of √5

• Find the cumulative probability for 8 in a binomial distribution with n = 20 and p = 0.5.

The figure shows the probability distribution of a discrete random variable X. Note that the cursor is on the histogram bar representing a value of 6. Which of the following best describes this random variable?

• Binomial with n = 8, p = 0.1

• Binomial with n = 8, p = 0.3

• Binomial with n = 8, p = 0.8

• Geometric with p = 0.2

How many outcomes should each trial have to use a Binomial Distribution?

• It depends

• 1

• 2

• Any number

The Binomial Distribution requires a ​ (a)   number of ​ (b)   trials

• fixed

• independent

• random

• dependent

• changeable