Quick questions on The normal distribution explained: H2 Mathematics Probability and Statistics

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What are combining normal variables?

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X \sim \mathrm{N}(\mu_X, \sigma_X^2)

and

Y \sim \mathrm{N}(\mu_Y, \sigma_Y^2)

are independent, then

aX + bY

is normal with mean

a\mu_X + b\mu_Y

and variance

a^2\sigma_X^2 + b^2\sigma_Y^2

(variances add, with squared coefficients).

What is sign error in standardising?

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Z = \dfrac{X - \mu}{\sigma}

; a value below the mean gives a negative

z

What is q1?

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For

X \sim \mathrm{N}(100, 15^2)

, find the

z

-score of

X = 130

. [1 mark]

What is q2?

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For

Z \sim \mathrm{N}(0, 1)

, find

\mathrm{P}(Z > 1)

. [2 marks]

What is q3?

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Independent variables

X \sim \mathrm{N}(5, 4)

and

Y \sim \mathrm{N}(3, 9)

. State the distribution of

X + Y

. [2 marks]

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