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These are the Transum resources related to the statement: "The normal distribution and curve. Properties of the normal distribution. Diagrammatic representation. Normal probability calculations. Inverse normal calculations".

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

Here are some exam-style questions on this statement:

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*The heights of palm trees along a beach are normally distributed with a mean of 4.55m and a standard deviation of 0.37m.*" ... more - "
*Eels are elongated fish, ranging in length from 5cm to 4m. In a certain lake the length of the eels are normally distributed with a mean of 84cm and a standard deviation of 18cm. Eels are classified as giant eels if they are more than 120 cm long.*" ... more - "
*A group of students sat a Biology examination and a Computer Studies examination. The students' marks in the Biology examination are normally distributed with a mean of 70 and a standard deviation of 9.*" ... more - "
*The weights of players in a sports league are normally distributed with a mean of 75.2 kg, (correct to three significant figures). It is known that 75% of the players have weights between 67 kg and 80 kg. The probability that a player weighs less than 67 kg is 0.05.*" ... more - "
*A random variable \(X\) is normally distributed with \(\mu=250\) and \(\sigma=25\).*" ... more - "
*The weights in grams of 98 mice are shown in the cumulative frequency diagram. The heaviest mouse weighted 160g.*" ... more - "
*The length, \(X\) minutes , of a certain category of online video is normally distributed with a mean of 28.*" ... more - "
*The length of Costlow's bâtard bread loaves in centimetres is normally distributed with mean \( \mu \). The following table shows probabilities for values of \(L\).*" ... more

Click on a topic below for suggested lesson starters, resources and activities from Transum.

If you would like to interact with the graph of the normal distribution you will find it waiting for you on the Graph Plotter page (you will need to rescale the axes).

The syllabus also mentions that students should be aware of the natural occurrences of the normal distribution. Students should be aware that approximately 68% of the data lies between one standard deviation above the mean and one standard deviation below the mean. Similarly 95% lies within two standard deviations of the mean and 99.7% lies within three.

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