<p><strong>In this question you should state clearly the values of the parameters of any normal distributions that you use.</strong></p>
<p>The masses, in grams, of apples and pears have the independent distributions $N\left( 260,\ {{15}^{2}} \right)$ and $N\left( 210,\ {{10}^{2}} \right)$ respectively.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find the probability that the mass of a randomly chosen apple is at least $250$ grams.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the probability that the mass of a randomly chosen apple differs from the mass of a randomly chosen pear by more than $55$ grams.</span></div><p style="text-align: right;">[2]</p></li></ol>
<p>A certain recipe requires $5$ apples and $6$ pears. The recipe requires the apples and pears to be prepared by removing the cores. This process reduces the mass of each apple by $5\%$ and the mass of each pear by $15\%$.</p>
<ol class="abc-list" start="3"><li><div class="list-item-content"><span class="list-item-text">Find the probability that the total mass, after preparation, of $5$ randomly chosen apples and $6$ randomly chosen pears is at least $2.3$ kilograms.</span></div><p style="text-align: right;">[3]</p></li><li><div class="list-item-content"><span class="list-item-text">Find $\mathrm{P}\left( 3\left( 0.7A \right)-0.8\left( {{B}_{1}}+{{B}_{2}} \right)>200 \right)$. Explain, in the context of this question, what your answer possibly represents.</span></div><p style="text-align: right;">[4]</p></li></ol>

**In this question you should state clearly the values of the parameters of any normal distributions that you use.**

The masses, in grams, of apples and pears have the independent distributions $N\left( 260,\ {{15}^{2}} \right)$ and $N\left( 210,\ {{10}^{2}} \right)$ respectively.

Find the probability that the mass of a randomly chosen apple is at least $250$ grams.

Find the probability that the mass of a randomly chosen apple differs from the mass of a randomly chosen pear by more than $55$ grams.

A certain recipe requires $5$ apples and $6$ pears. The recipe requires the apples and pears to be prepared by removing the cores. This process reduces the mass of each apple by $5\%$ and the mass of each pear by $15\%$.

Find the probability that the total mass, after preparation, of $5$ randomly chosen apples and $6$ randomly chosen pears is at least $2.3$ kilograms.

Find $\mathrm{P}\left( 3\left( 0.7A \right)-0.8\left( {{B}_{1}}+{{B}_{2}} \right)>200 \right)$. Explain, in the context of this question, what your answer possibly represents.

2023 ASRJC P2 Q9

2023 ASRJC P2 Q9

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