What is a binomial distribution?

• A binomial distribution is a?discrete probability distribution
• The?discrete random variable?follows a?binomial distribution?if it?counts the number of successes?when an experiment satisfies the conditions:

What are the important properties of a binomial distribution?

Square root to get the standard deviation

• The distribution can be represented visually using a vertical line graph
  • If?p?is?close to 0?then the graph has a?tail to the right
  • If?p?is?close to 1?then the graph has a?tail to the left
  • If?p?is?close to 0.5?then the graph is?roughly symmetrical
  • If?p =?0.5?then the graph is?symmetrical

How do I set up a binomial model?

• Identify?what a?trial?is in the scenario
  • For example: rolling a dice, flipping a coin, checking hair colour
• Identify?what the?successful outcome?is in the scenario
  • For example: rolling a 6, landing on tails, having black hair
• Make sure you?clearly state?what your?random variable?is
  • For example, let?X??be the number of students in a class of 30 with black hair

What can be modelled using a binomial distribution?

• Anything that satisfies the?four conditionsAs long as the population is large and the sample is random then it can be assumed that each person has a 30% chance of having blue eyes

What can not be modelled using a binomial distribution?

• Anything where the number of trials is?not fixed?or is?infinite
  • The number of emails received in an hour
  • The number of times a coin is flipped until it lands on heads
• Anything where the outcome of?one trial affects?the outcome of the?other trials
  • The number of caramels that a person eats when they eat 5 sweets from a bag containing 6 caramels and 4 marshmallows
    • If you eat a caramel for your first sweet then there are less caramels left in the bag when you choose your second sweet
• Anything where there are?more than two outcomes?of a trial
  • A person's shoe size
  • The number a dice lands on when rolled
• Anything where the?probability of success changes
  • The number of times that a person can swim a length of a swimming pool in under a minute when swimming 50 lengths
    • The probability of swimming a lap in under a minute will decrease as the person gets tired