<p><strong>In this question, you should state clearly the values of the parameters of any normal distribution you use.</strong><br>A supermarket sells two types of durians, D$26$ and Civet King. The durians are sold by weight. The masses, in kilograms, of D$26$ and Civet King are modelled as having normal distributions. The means and standard deviations of these distributions, and the selling prices, in $\$$ per kilogram, are shown in the following table.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr><th style="text-align: center; --cell-justify: center"></th><th style="text-align: center; --cell-justify: center">Mean (kg)</th><th style="text-align: center; --cell-justify: center">Standard Deviation (kg)</th><th style="text-align: center; --cell-justify: center">Selling price ($\$$ per kg)</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">D26</td><td style="text-align: center; --cell-justify: center">$1.8$</td><td style="text-align: center; --cell-justify: center">$0.02$</td><td style="text-align: center; --cell-justify: center">$9$</td></tr><tr><td style="text-align: center; --cell-justify: center">Civet King</td><td style="text-align: center; --cell-justify: center">$\mu$</td><td style="text-align: center; --cell-justify: center">$\sigma$</td><td style="text-align: center; --cell-justify: center">$18$</td></tr></tbody></table></div></div>
<ol class="abc-list"><li data-list-item-id="imported-item-block-2-item-0" data-list-item-path="imported-item-block-2-item-0"><div class="list-item-paragraph"><p>Find the probability that the mass of a randomly selected D$26$ is less than $1.76\text{ kg}$.</p><span class="inline-marks">[2]</span></div></li><li data-list-item-id="imported-item-block-2-item-1" data-list-item-path="imported-item-block-2-item-1"><div class="list-item-paragraph">It is known that&nbsp;$65\%$ of the Civet King have a price greater than $\$32.16$ and $25\%$ of them have a price less than $\$31.98$. Show that&nbsp;$\mu = 1.8$ and $\sigma = 0.035$, correct to $2$ significant figures.<span class="inline-marks">[3]</span></div></li><li data-list-item-id="imported-item-block-2-item-2" data-list-item-path="imported-item-block-2-item-2"><div class="list-item-paragraph"><p>A customer buys $4$ D$26$ durians and $3$ Civet King durians. Find the probability that the total cost of his purchase is more than $\$160$.</p><span class="inline-marks">[4]</span></div></li><li data-list-item-id="imported-item-block-2-item-3" data-list-item-path="imported-item-block-2-item-3"><div class="list-item-paragraph"><p>State an assumption needed for your calculations in part <strong>(iii)</strong>.</p><span class="inline-marks">[1]</span></div></li></ol>

**In this question, you should state clearly the values of the parameters of any normal distribution you use.**
A supermarket sells two types of durians, D$26$ and Civet King. The durians are sold by weight. The masses, in kilograms, of D$26$ and Civet King are modelled as having normal distributions. The means and standard deviations of these distributions, and the selling prices, in $\$$ per kilogram, are shown in the following table.

<p>Find the probability that the mass of a randomly selected D$26$ is less than $1.76\text{ kg}$.</p>

It is known that $65\%$ of the Civet King have a price greater than $\$32.16$ and $25\%$ of them have a price less than $\$31.98$. Show that $\mu = 1.8$ and $\sigma = 0.035$, correct to $2$ significant figures.

<p>A customer buys $4$ D$26$ durians and $3$ Civet King durians. Find the probability that the total cost of his purchase is more than $\$160$.</p>

<p>State an assumption needed for your calculations in part <strong>(iii)</strong>.</p>

	Mean (kg)	Standard Deviation (kg)	Selling price (\(\$\) per kg)
D26	\(1.8\)	\(0.02\)	\(9\)
Civet King	\(\mu\)	\(\sigma\)	\(18\)

2025 TGM P2 Q9

2025 TGM P2 Q9