Statistical Distributions

Scheme of work: Year 12 A-Level: Applied: Statistics: Statistical Distributions

Prerequisite Knowledge

  • Understand the meanings of terms used in probability;
  • Calculate probabilities of single events;
  • Identify and use sample spaces
  • Draw and interpret Venn diagrams;
  • Understand mutually exclusive and independent events and determine whether two events are independent
  • Use and understand tree diagrams.

Success Criteria

  • Use simple, discrete probability distributions, including the binomial distribution;
  • Identify the discrete uniform distribution;
  • Calculate probabilities using the binomial distribution.
  • Calculate cumulative probabilities using the binomial distribution

Key Concepts

  • Students need to understand what a discrete random variable is.
  • A probability distribution can be a table, graph or mass function. Students need to be able to convert between the three and understand the specific benefits of each.
  • The expected frequency E(X) is the average frequency at which you expect an event to occur. Students can calculate E(X) using the STAT mode on a ClassWiz calculator.
  • Students need to know a binomial model can only be used to model a distribution when:
    • there are a fixed number of trials
    • there are precisely two outcomes
    • there is a constant probability of success
    • the trials are independent of each other
  • Students need to be confident using the Binomial PD and CD functions on a Classwiz calculator as well as the tables provided in the formula booklet.
  • The tables in the formula booklet can be recreated using the List function on a Classwiz calculator.

Common Misconceptions

  • Students are often confused about when to use Binomial PD and Binomial CD on a Classwiz calculator.
  • Students often struggle using the cumulative function to work out probabilities greater than or at least a specific value.
  • Students often struggle to set up a pair of simultaneous equations from a probability distribution. To do this, they use the expected value and the sum of the probabilities equalling one.

Statistical Distributions Resources

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