IB AA SL and HL: core and optional content Core: two individual watermelon probabilities and the per

Question

IB AA SL and HL: core and optional content

Core: two individual watermelon probabilities and the percentile c. Optional: total masses and total costs.

A market stall sells two types of fruit, watermelons and mangos. The masses, in kg, of each type of fruit have independent normal distributions. The means and standard deviations of these distributions, and the selling prices, in $\$ $ per kg, are shown in the following table.

	Mean (kg)	Standard deviation (kg)	Price ($\$ $ per kg)
Watermelon	$4.2$	$0.6$	$4$
Mango	$0.8$	$0.1$	$2.50$

Find the probability that two randomly chosen watermelons each have a mass between $3$ and $5$ kg.[2]
$20\%$ of watermelons weigh less than $c$ kg. Find $c$.[2]
Find the probability that the total mass of $2$ randomly chosen watermelons is within $\pm 0.5$ kg of the total mass of $10$ randomly chosen mangoes.[4]
Find the probability that the total cost of $2$ randomly chosen watermelons and $3$ randomly chosen mangoes is more than $\$ 42$.[4]

Accepted Answer

(a) $0.785$ (b) $3.70$ kg (c) $0.384$ (d) $0.242$

	Mean (kg)	Standard deviation (kg)	Price (\(\$ \) per kg)
Watermelon	\(4.2\)	\(0.6\)	\(4\)
Mango	\(0.8\)	\(0.1\)	\(2.50\)

2024 YIJC H1 Q12

2024 YIJC H1 Q12

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