<p>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.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr style="height: 28px;"><th style="height: 28px; min-height: 28px; text-align: left; --cell-justify: flex-start"></th><th style="height: 28px; min-height: 28px; text-align: center; --cell-justify: center"><p>Mean (kg)</p></th><th style="height: 28px; min-height: 28px; text-align: center; --cell-justify: center"><p>Standard deviation (kg)</p></th><th style="height: 28px; min-height: 28px; text-align: center; --cell-justify: center"><p>Price per kg</p></th></tr></thead><tbody><tr style="height: 28px;"><td style="height: 28px; min-height: 28px; text-align: center; --cell-justify: center"><p>XO</p></td><td style="height: 28px; min-height: 28px; text-align: center; --cell-justify: center">$2.5$</td><td style="height: 28px; min-height: 28px; text-align: center; --cell-justify: center">$0.8$</td><td style="height: 28px; min-height: 28px; text-align: center; --cell-justify: center">$\$12$</td></tr><tr style="height: 28px;"><td style="height: 28px; min-height: 28px; text-align: center; --cell-justify: center"><p>D24</p></td><td style="height: 28px; min-height: 28px; text-align: center; --cell-justify: center">$2.0$</td><td style="height: 28px; min-height: 28px; text-align: center; --cell-justify: center">$0.5$</td><td style="height: 28px; min-height: 28px; text-align: center; --cell-justify: center">$\$7$</td></tr></tbody></table></div></div>
<ol class="i-list"><li><div class="list-item-paragraph">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.<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">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 $\$15$.<span class="inline-marks">[4]</span></div></li><li><div class="list-item-paragraph">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 $0.9$.<span class="inline-marks">[4]</span></div></li></ol>

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.

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.

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 $\$15$.

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 $0.9$.

2013 MI P2 Q10

2013 MI P2 Q10

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