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Mathematical Methods · Unit 4 · Continuous random variables and the normal distribution · Normal distributions

Identify contexts, e.g. naturally occurring variations, that are suitable for modelling by normal random variables.

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Question 1

A farmer measures the mass of eggs produced by her flock of hens over a one-month period. The distribution of egg masses is approximately symmetric and bell-shaped, with no extreme outliers. The mean mass is 62 g and the standard deviation is 4 g. (a) Identify whether the mass of eggs can be modelled by a normal random variable, and state the reason for your choice. [1 mark] (b) Using the normal model, estimate the percentage of eggs with a mass between 58 g and 66 g. [2 marks]

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Question 2

Which of the following phenomena is most suitable to model using a normal distribution?

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Question 3

Which of the following scenarios describes a variable that would be most appropriately modelled by a normal distribution?

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