3.4 the standard normal distribution, 3.5 Finding µ and σ

It often useful to standardise normally distributed random variables.

How do you do this?

By coding the data so that it can be modelled by the standard normal distribution

What is the mean and standard deviation of the standard normal distribution?

• The mean is 0

• The standard deviation is 1

What is the notation for the standard normal variable?

Z~ N(0, 1²)

If X~N(µ, σ²) is a normal random variable with mean µ and standard deviation σ, then what formula can we use to code X?

Z= (X - µ) / σ

Links!

What mean and standard deviation are the resulting z-values normally distributed with?

Mean: 0

Standard deviation: 1

Example 6

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Example 7

You might need to find an unknown ____ or ________ for a normally distributed variable

You might need to find an unknown mean or standard deviation for a normally distributed variable

Example 8

Example 9a

Example 9b

Example 10