The mass, in kg, of durians and watermelons sold at a fruit stall follow normal distributions with t

Question

The mass, in kg, of durians and watermelons sold at a fruit stall follow normal distributions with the following data.

	Mass (kg)	Variance (kg${^2}$)
Durian	$3.21$	$0.65$
Watermelon	$6.25$	$0.25$

Find the probability that

Four randomly selected durians are heavier than twice a randomly selected watermelon.
Two randomly selected durians are heavier than a randomly selected watermelon by at most 500 g.
The difference in mass between a randomly selected durian and a randomly selected watermelon is less than 3.5 kg.
The total mass of three randomly selected durians is less than 9 kg.
The mass of three randomly selected durians all weighed less than 3 kg.

Explain why answer in (iv) is higher than answer in (v).

Modelling assumption for this exercise: masses of all distinct selected fruits are mutually independent and follow the stated distribution for their type.

Accepted Answer

(i) $0.571$ (ii) $0.159$ (iii) $0.686$ (iv) $0.326$ (v) $0.0627$ Explanation: Event (v) is a proper subset of event (iv), so (iv) has the greater probability.

	Mass (kg)	Variance (kg\({^2}\))
Durian	\(3.21\)	\(0.65\)
Watermelon	\(6.25\)	\(0.25\)

Probability Problems Involving Normal Distributions

Probability Problems Involving Normal Distributions

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