2010 A-level H2 Mathematics (9740) Paper 2 Question 9 Suggested Solutions

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

(i)
Y -2X \sim \text{N}(40, 7400)

\text{P} (Y>2X)

= \text{P} (Y-2X>0)

= 0.681

(ii)
0.05Y + 0.12X \sim \text{N}(41.6, 21.96)

\text{P} (0.05Y + 0.12X > 45)

= 0.234

(iii)
Let X_1, X_2 = number of peak rate calls over the two three-month periods.

0.12(X_1+X_2) \sim \text{N} (43.2, 25.92)

\text{P}(0.12(X_1+X_2) > 45)

= 0.362

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