Normal Distribution | CIE AS Maths: Probability & Statistics 1 Exam Questions 2020

1a

1 mark

A continuous random variable can take any value within a given range. Many naturally occurring continuous quantities can be modelled using the Normal Distribution, for example the height of human beings; the mass of new born puppies or the distribution of all A Level maths exam results.

Give a different example of a quantity that could be modelled using the normal distribution.

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1b

3 marks

The graph of the normal distribution has a characteristic bell shape that is symmetrical about the mean, $μ$ . If $X$ has a normal distribution with a mean, $μ$ , and variance, $σ^{2}$ , then it can be written as $X ~ N (μ, σ^{2}) .$

For $X ~ N (μ, σ^{2})$ , state:

(i)

P (X < μ)

(ii)

P (X \geq μ)

(iii)

P (X = μ)

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1c

1 mark

Using your answers to part (b), or otherwise, explain why there is no difference between $\geq$ and $>$ or $\leq$ and $<$ when calculating normal probabilities.

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Normal Distribution (CIE AS Maths: Probability & Statistics 1)

Exam Questions

1. Data Presentation & Interpretation

1.1 Statistical Measures

1.2 Representation of Data

1.3 Working with Data

2. Probability

2.1 Basic Probability

2.2 Permutations & Combinations

2.3 Further Probability

3. Statistical Distributions

3.1 Probability Distributions

3.2 Binomial & Geometric Distribution

3.3 Normal Distribution

3.4 Working with Distributions