A fruit stall sells $2$ types of durians, XO and D24. For each type of durian, a randomly chosen d

Question

A fruit stall sells $2$ types of durians, XO and D24. For each type of durian, a randomly chosen durian has a mass that is normally distributed with mean and standard deviation, as well as unit price as shown in the following table. Mean (kg) Standard deviation (kg) Price per kg XO $2.5$$0.8$$\$12$ D24 $2.0$$0.5$$\$7$ Find the probability that the total mass of $2$ randomly chosen XO durians is more than $3$ times the mass of a randomly chosen D24 durian.[3] Find the probability that the price of a randomly chosen XO durian differs from the price of a randomly chosen D24 durian by less than $\$15$.[4] A sample of $n$ XO durians is randomly chosen. Find the least value of n such that the probability that the mean mass is more than $2.25$ kg exceeds $0.9$.[4] Modelling assumption for this exercise: masses of all distinct selected durians are mutually independent and follow the stated distribution for their type.

Accepted Answer

(i) $0.297$ (ii) $0.460$ (iii) $n=17$

	Mean (kg)	Standard deviation (kg)	Price per kg
XO	\(2.5\)	\(0.8\)	\(\$12\)
D24	\(2.0\)	\(0.5\)	\(\$7\)

2013 MI P2 Q10

2013 MI P2 Q10

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