THE BINOMIAL DISTRIBUTION

• What is the binomial distribution used for?

  To model situations with two outcomes
• What are the two possible outcomes in a binomial distribution?

  Success and failure
• What does the parameter q represent in a binomial distribution?

  The probability of failure
• What is the relationship between p and q in a binomial distribution?

  q = 1 - p
• What does the notation X ~ B(n, p) signify?

  X has a binomial distribution with parameters n and p
• If you throw a dice 20 times, what is the probability of getting a six?

  $\frac{1}{6}$
• What is the formula for calculating the probability that X takes the value r in a binomial distribution?

  P(X = r) = C(n, r) p^r q^{n-r}
• What does C(n, r) represent in the binomial probability formula?

  The binomial coefficient
• How is the binomial coefficient C(n, r) calculated?

  C(n, r) = $\frac{n!}{r!(n-r)!}$
• How can you find binomial probabilities using a calculator?

  Enter values for n and p
• What is a cumulative binomial probability?

  Probability of a range of results
• How would you find P(X ≤ 5) for a binomial distribution?

  Use the cumulative probability function
• What does P(X ≥ 7) equal if only P(X ≤ n) is available?

  P(X ≥ 7) = 1 - P(X ≤ 6)
• What does 'five or fewer sixes' mean in probability terms?

  P(X ≤ 5)
• What does 'fewer than five sixes' mean in probability terms?

  P(X < 5)
• What does 'five or more sixes' mean in probability terms?

  P(X ≥ 5)
• What does 'more than five sixes' mean in probability terms?

  P(X > 5)
• How is the mean of a binomial distribution calculated?

  Mean = np
• If you throw a dice 50 times, what is the mean number of sixes?

  $8.33$