Statistical Distributions

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

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.

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

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.

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.