2013 A-level H2 Mathematics (9740) Paper 2 Question 6 Suggested Solutions

By KS Teng

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
Y~\sim~N(\mu, {\sigma}^{2})

P(Y \textless 2a ) = 0.95

\frac{2a-\mu}{\sigma} = 1.64485

2a - \mu = 1.64485 \sigma \rightarrow 1

P(Y \textless a ) = 0.25

\frac{a-\mu}{\sigma} =-0.67449

a-\mu =-0.67449 \sigma \rightarrow 2

Consider (1) - (2)

a = 2.31934 \sigma \Rightarrow \sigma = \frac{a}{2.31934}

\mu =a + 0.67449(\frac{a}{2.31934})

\therefore, \mu \approx 1.29a ~\mathrm{and}~ k = 1.29

KS Comments:

This question is well attempted.

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