The binomial distribution is an example of a discrete probability distribution. The normal distribution is an example of a?continuous?probability distribution.

What is a continuous random variable?

• A continuous random variable (often abbreviated to CRV) is a random variable that can take?any value?within a range of infinite values
  • Continuous random variables?usually measure?something
  • For example, height, weight, time, etc

What is a continuous probability distribution?

What is a normal distribution??

• A normal distribution is a?continuous probability distribution
• • μ?is the?mean
  • σ²?is the?variance
  • σ?is the?standard deviation
• If the?mean?changes then the graph is?translated horizontally
• If the?variance?changes then the graph is?stretched horizontally
  • A?small variance?leads to a?tall?curve with a?narrow?centre
  • A?large variance?leads to a?short?curve with a?wide?centre

What are the important properties of a normal distribution?

• The?mean?is?μ
• The?variance?is?σ²
  • If you need the?standard deviation?remember to square root this
• The normal distribution is symmetrical about
  • Mean = Median = Mode =?μ
• There are the results:
  • Approximately?two-thirds (68%)?of the data lies within?one standard deviation?of the mean (μ?±?σ)
  • Approximately?95%?of the data lies within?two standard deviations?of the mean?(μ?±?2σ)
  • Nearly?all of the data (99.7%)?lies within?three standard deviations?of the mean?(μ?±?3σ)

What can be modelled using a normal distribution?

• A lot of real-life continuous variables can be modelled by a normal distribution provided that the population is large enough and that the variable is?symmetrical?with?one mode
  • This fact allows us to model variables that are not defined for all real values such as height and weight

What can not be modelled using a normal distribution?

• Variables which have?more than one mode?or?no mode
  • For example: the number given by a random number generator
• Variables which are?not symmetrical
  • For example: how long a human lives for