# 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

### Mr Mathematics Blog

#### Sequences and Series

Edexcel A-Level Mathematics Year 2: Pure 2: Algebraic Methods

#### T- Formulae

Scheme of work: A-Level Further Mathematics: Further Pure 1: The t – formulae

#### Regression, Correlation and Hypothesis Testing

A-Level Scheme of work: Edexcel A-Level Mathematics Year 2: Statistics: Regression, Correlation and Hypothesis Testing