2013 A-level H1 Mathematics (8864) Question 11 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)
Let X denote the mass of food content in a type A packet, in grams
Let Y denote the mass of food content in a type B packet, in grams.

X ~\sim~ \mathrm{N}(1000, \sigma^{2})
Y ~\sim~ \mathrm{N}(1010,428)

\mathrm{P} (X < 990) = 0.2
\mathrm{P} (Z < \frac{990 - 1000}{\sigma}) = 0.2
-\frac{10}{\sigma} = -0.84162
\sigma = 11.8

(ii)
\mathrm{P} (Y < 1000) = 0.314

(iii)
Y - X ~\sim~ \mathrm{N}(10, 569.18)

\mathrm{P} (Y > X) = \mathrm{P} (Y - X > 0) = 0.662

KS Comments

Students are expected to show the workings for expectation and variance clearly here.

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