Binomial Random Variables

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

Find the mean of the probability distribution.

• 85
• 83.2
• 87.1
• 84.4

Which one of these variables is a continuous random variable?

• The time it takes a randomly selected student to complete an exam.
• The number of tattoos a randomly selected person has.
• The number of women taller than 68 inches in a random sample of 5 women. 
• The number of correct guesses on a multiple choice test. 

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

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

If you were to flip a coin 20 times, what is the probability you would get exactly 10 heads?

• 50%

• 17.62%

• 58.81%

• 41.19%

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