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]

Accepted Answer

$n = 17$

2013 MI P2 Q10

2013 MI P2 Q10

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