3.15 N: Statistical Distributions

• The binomial distribution represents the probabilities of success or failure in independent trials
• Two important discrete distributions are the binomial and the Poisson
• A statistical distribution describes the probabilities of different outcomes
• The Poisson distribution is used to model the number of events in a fixed interval.


  True
• Match the distribution with its key characteristic:

  Binomial ↔️ Fixed trials

  Poisson ↔️ Fixed interval
• Under what conditions can the binomial distribution be applied?

  Fixed trials, independent events
• What are the two possible outcomes in each trial of the binomial distribution?

  Success or failure
• How many trials are there in the binomial distribution?

  Fixed
• The binomial distribution models the probability of success in a fixed number of independent trials
• Match the distribution with its characteristic:

  Binomial ↔️ Fixed number of trials

  Poisson ↔️ Fixed time/space interval

  Normal ↔️ Continuous variables
• The normal distribution is symmetric and peaks at the mean
• Match the statistical distribution with its application:

  Normal ↔️ Inferential statistics

  Binomial ↔️ Quality control

  Poisson ↔️ Call center volume
• The binomial distribution requires a fixed number of independent trials.


  True
• In the binomial distribution, each trial is dependent on the others.

  False
• The Poisson distribution is continuous.

  False
• In the Poisson distribution, events are considered independent.
• What are the two parameters that define the normal distribution?

  Mean and standard deviation
• Steps to use a z-table to find probabilities:

  1️⃣ Convert the raw value to a z-score

  2️⃣ Refer to the z-table for the probability

  3️⃣ Adjust the probability based on the question
• The normal distribution is symmetric.


  True
• The Poisson distribution models events in a fixed interval
• Steps to calculate probabilities using statistical tables for the normal distribution

  1️⃣ Convert the raw value to a z-score using the formula: z = (x - μ) / σ

  2️⃣ Refer to the z-table to find the corresponding probability

  3️⃣ Adjust the probability based on whether the question asks for less than, greater than, or between values
• The normal distribution is used in inferential statistics.


  True
• To find the probability of a value between two z-scores, subtract the lower probability from the higher
• What does a statistical distribution describe?

  Probabilities of outcomes
• The Poisson distribution models the number of events in a fixed interval.


  True
• Match the discrete distribution with its definition:

  Binomial ↔️ Successes in fixed trials

  Poisson ↔️ Events in fixed interval
• The normal distribution is bell-shaped and symmetric.


  True
• Discrete distributions deal with countable outcomes, while continuous distributions deal with measurements on a continuous scale.
• The Poisson distribution assumes that events occur independently and at a constant average rate.


  True
• The probability of success in the binomial distribution must be constant across trials.


  True
• Each trial in the binomial distribution is dependent on the previous trial.

  False
• Match the distribution with its definition:

  Binomial ↔️ Success probabilities in fixed trials

  Poisson ↔️ Events in a fixed interval

  Normal ↔️ Probabilities of continuous variables
• The independence of trials is a key assumption of the binomial distribution.


  True
• What is the average rate parameter in the Poisson distribution denoted by?

  $\lambda$
• Which continuous distribution is skewed?

  Exponential
• The binomial and Poisson distributions are both types of discrete
• Match the distribution characteristic with its corresponding distribution:

  Fixed trials, independent events ↔️ Binomial

  Constant average rate, random events ↔️ Poisson

  Bell-shaped, symmetric ↔️ Normal
• The probability of success in the binomial distribution is constant across trials.
• What parameter defines the average rate of events in the Poisson distribution?

  λ
• Continuous distributions model the probability of variables taking on discrete values.

  False