Research Methods 2

Week 5: The Properties of the Normal distribution

Aims

To explain, in quantitative terms, what it means for a variable to have a Normal distribution.

To understand that it is the area under the bell-shaped Normal curve that is most readily interpreted.

To know that the area under the whole curve is 1.  Also that the area under the curve up to a given point, X, is the proportion of the population with values that are less than X.

To be able to use simple arguments of symmetry to deduce how other quantities of interest, such as the proportion of the population with values between two given points, might be calculated.

To know the 68-95-99.7 rule for the Normal distribution.

This week there is only one document to be studied and one exercise sheet to be attempted.  You will be studying the Normal distribution in a little more depth and learning some of the quantitative implications that follow from an assumption that a variable has a Normal distribution.  Some of the facts will be of use in their own right but a good deal of what you learn this week is of value because of how we will use it in the next few weeks.

• Study the document Quantitative use of the Normal curve located in the Learning Materials folder, which explains some of the quantitiative features of the Normal curve.
• Attempt the questions in Exercise Sheet 1, which is in the Formative Assessment Activities folder.
• You should check your answers by referring to the Solutions to Exercise Sheet 1, also in the Formative Assessment Activities folder.