4.11 Parameters for a Binomial Distribution

• In a binomial distribution, the number of trials is predetermined.


  True
• The probability of success remains constant for each trial in a binomial distribution.


  True
• What does the parameter 'n' represent in a binomial distribution?

  Number of trials
• What is the binomial coefficient represented by in the binomial PMF?

  $\binom{n}{k}$
• What is the probability of success 'p' in a binomial distribution?

  Constant for each trial
• If a fair coin is flipped, the probability of getting heads on a single flip is $p =$$0.5$.


  True
• The binomial coefficient in the PMF is denoted as $\binom{n}{k}$
• In a binomial distribution, $n$ represents the number of trials
• If you flip a coin 10 times, the value of $n$ in the binomial distribution is 10
• The parameters of a binomial distribution are the number of trials ($n$) and the probability of success
• The binomial coefficient $\binom{n}{k}$ is used in the PMF of a binomial distribution.


  True
• What is a key condition for binomial trials regarding their independence?

  Trials must be independent
• What are the two parameters of a binomial distribution?

  $n$ and $p$
• What does $n$ represent in the binomial distribution when flipping a coin 10 times?


  10
• What is the variable in a binomial distribution that depends on the binomial formula?

  $X$
• What is the probability of success in a binomial distribution if 25 students take a test and 20 pass?

  p = 0.8</latex>
• What is a key characteristic of binomial trials?

  Independence
• What is the formula for the probability mass function (PMF) of a binomial distribution?

  P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}</latex>
• The parameter 'p' in a binomial distribution represents the probability of success in each trial.

  True
• Conditions that must be met for a binomial distribution:

  1️⃣ The number of trials ($n$) is fixed.

  2️⃣ The trials are independent.

  3️⃣ Each trial has two possible outcomes: success or failure.

  4️⃣ The probability of success ($p$) is constant for each trial.
• In a binomial distribution, n represents the number of trials
• A binomial distribution is a discrete probability distribution that describes the number of successes
• In a coin flip repeated 10 times with $p =$$0.5$, the binomial distribution has $n =$$10$.


  True
• What does $p$ represent in a binomial distribution?


  Probability of success
• What is the variable in a binomial distribution?

  $X$ (number of successes)
• The probability of success ($p$) must remain constant for each trial in a binomial distribution.


  True
• The parameter $n$ represents the fixed number of independent trials
• In a binomial distribution, p</latex> represents the probability of success
• In a binomial distribution with 10 coin flips and $p =$$0.5$, the variable is the number of heads
• If 100 light bulbs are tested and 3 are defective, $n =$$100$ and $p =$$0.03$ in a binomial distribution
• A binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials
• Each trial in a binomial distribution results in either success or failure
• Match the binomial parameter with its description:

  $n$ ↔️ Total number of independent trials

  $p$ ↔️ Probability of success in each trial
• In a binomial distribution, the number of trials ($n$) is predetermined
• The number of trials 'n' in a binomial distribution must be a fixed number.

  True
• What does 'p' represent in a binomial distribution?

  Probability of success
• What is the probability mass function (PMF) of a binomial distribution?

  $P(X = k) =$$\binom{n}{k} p^{k} (1 - p)^{n - k}$
• What are the parameters of a binomial distribution?

  n and p
• Steps to determine if a scenario follows a binomial distribution

  1️⃣ Check for a fixed number of trials

  2️⃣ Verify independence of trials

  3️⃣ Confirm two possible outcomes (success or failure)

  4️⃣ Ensure constant probability of success
• In a binomial distribution, the trials must be independent.


  True