When should I use a binomial distribution?

• A random variable that follows a?binomial distribution?is a?discrete random variable
• A binomial distribution is used when the random variable?counts something
  • The number of successful trials
  • The number of members of a sample that satisfy a criterion (satisfying the criteria can be seen as a successful trial)
• There are?four conditions?that?X?must fulfil to follow a binomial distribution
  • There is a?fixed finite number of trials (n)
  • The trials are?independent
  • There are?exactly two outcomes?of each trial (success or failure)
  • The?probability of success (p)??is constant

When should I use a geometric distribution?

• A random variable that follows a?geometric distribution?is a?discrete random variable
• A geometric distribution is used when the random variable?counts something
  • The number of trials until a successful trial
• The conditions that?X??must fulfil to follow a geometric distribution are exactly the same as for a binomial distribution except there is?no fixed number of trials
  • Instead, the trials will continue until the?first time a?success?occurs

When should I use a normal distribution?

• A random variable that follows a?normal distribution?is a?continuous random variable
• A normal distribution is used when the random variable?measures something?and the distribution is:
  • Symmetrical
  • Bell-shaped
• A normal distribution can be used to model real-life data provided the?histogram?for this data is?roughly symmetrical and bell-shaped
  • If the variable is normally distributed then as more data is collected the outline of the histogram should get smoother and resemble a normal distribution curve

Can the binomial distribution and the normal distribution be used in the same question?

• Some questions might require you to?first use the normal distribution?to find the?probability of success?and then use the?binomial distribution
  • Remember a discrete distribution is either a binomial or geometric distribution
• The key is to make sure you are very clear about what each?parameter/variable represents