Binomial Variables

Which descriptions are true for a binomial distribution?

• 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

• The probabilities must add to 1

• each trial must be independent

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

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

• fixed

• independent

• random

• dependent

• changeable

Which of the following is NOT an assumption of the Binomial distribution?

• All trials must be independent.

• Each trial must be classified as a success or a failure.

• All trials are dependent on each other.

• The number of successes in the trials is counted.

Is the distribution below a probability distribution? Why or why not?

• Yes. All P(x) values are between 0 and 1, and ∑P(x) = 1

• No, not all P(x) values are between 0 and 1.

• No, ∑P(x) ≠ 1.

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 exactly 2 of the first 20 blood donors have Type B blood? 

• 0.316

• 0.282

• 0.001

• Not here

Classify by number of terms:
3x³ – 6x

• Monomial

• Binomial

• Trinomial

• 4-Term Polynomial

Which one of these variables is a binomial random variable?

• Time it takes a randomly selected student to complete a multiple choice exam

• Number of textbooks a randomly selected student bought this term 

• Number of women taller than 68 inches in a random sample of 5 women

• Number of CDs a randomly selected person owns

Is this binomial experiment? Shuffle a deck of 52 cards. Turn over the top card. Put the card back in the deck, shuffle again. Repeat the process 50 times. Let X = the number of aces you observe.

• Yes

• No, the trials are not independent.

• No, there are more than 2 outcomes