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Probability: the Independent School

In this activity students are presented with a variety of information regarding the number of students who study mathematics and/or physics. Students are asked to use this information to complete a Venn diagram. A complete solution to the problem is explained before a series of related challenges are posed...

Discrete Random Variables: DRVs from a Bag

This exercise is designed to ensure that students know how to find the expected value, E(X), and the variance, Var(X) for a discrete random variable, and that the probabilities in a probability distribution always add to one. Students are given a selection of numbers and are challenged to establish those...

Binomial Distribution: Most Likely Value

In this activity, students apply their knowledge of the binomial distribution to establish whether each of three rules, regarding the most likely outcome and the expected value, are true. The presentation contains a link to an applet which allows experimentation, and shows the binomial probabilities for various n...

Binomial Distribution: the Binomial Mean and Variance

This activity begins with the definition of the mean and the variance of a binomial distribution. Students are then challenged to take each definition and prove that they work for the binomial distribution B(3,p). The first task is for students to construct the probability distribution then calculate the mean and...

Binomial Distribution: Binomial Reverse

Most binomial questions define the binomial distribution and ask students to calculate the most likely value for x. In this activity, students are asked to explore whether the value for p can be found given the value for n and the most likely value for x. Subsequent pages of the presentation provide the solution to...

The Poisson Distribution: Poisson or Not?

In this resource, students are asked to consider data set in which the value of the mean is very close to the value of the variance. The aim of the resource is for students to understand that whilst mean being equal to variance indicates that the distribution may be a Poisson distribution that this not true in all...

The Poisson Distribution: Adding Two Poisson Distributions

In this resource, students consider whether two Poisson distributions can be added together to form a third Poisson distribution. The initial, discussion generating proposition is backed up by a proof. The resource also contains an accompanying spreadsheet on which students can run simulations to test the result....

The Poisson Distribution: a Close Approximation

In this activity, students are presented with a case in which the calculate probability is calculated using the Binomial and then the Poisson distribution. Each method produces results close to each other. Students are set the task of finding the value for n used. Subsequent slides reveal the solution.

This...

The Normal Distribution: the Coffee Problem

In this activity, students are posed the problem of how a coffee machine should be adjusted to meet certain criteria by either adjusting the mean value of the coffee produced or adjusting the standard deviation. The presentation ends showing the solution to the problem.

This resource is part of the Making...

Sampling and Hypothesis Testing using the Normal Distribution: Sampling

In this activity, students are given 100 natural numbers, all with value less than one hundred, and are asked to estimate the mean of the population by taking a number of samples, finding the mean of each sample and then finding the mean of the sample means.

This resource is part of the Making Stats Vital...