<p>To raise its profile, ABC Supermart devised a publicity where, if a customer has purchases of $\${}R$ or more in a single receipt, he is qualified to participate in a sure-win “Lucky Spin” game. In the game, the customer spins the first wheel (which is divided into $3$ equal parts) to see how much money he wins, then he spins a second wheel to see how much his winning is multiplied by.</p>
<figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/converted/1759565754081-gmwxv2hnvk.jpg" width="400" class="aligncenter" /></figure>
<p>For example, based on the illustration above, if the result from the first spin is “$\$10$”, and the result of the second spin is“$\times 4$”, then the person playing the game would have received $\$40$. </p>
<p>Let $X$ denote the amount won from playing the game.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Tabulate the probability distribution of $X$.</span></div><p style="text-align: right;">[2]</p></li><li><div class="list-item-content"><span class="list-item-text">ABC Supermart makes a profit of $40$% on all purchases made by customers. It wishes to use the profits generated from every qualifying receipt to offset the amounts given away in the game. Determine the value of $\${}R$ that the Supermart needs to set for a customer to qualify to play the game. Give your answer correct to the nearest dollar.</span></div><p style="text-align: right;">[3]</p></li><li><div class="list-item-content"><span class="list-item-text">Find the value of $\sigma$, the standard deviation of $X$. Hence find $\mathrm{P}\left( X<\sigma \right)$.</span></div><p style="text-align: right;">[3]</p></li></ol>

To raise its profile, ABC Supermart devised a publicity where, if a customer has purchases of $\${}R$ or more in a single receipt, he is qualified to participate in a sure-win “Lucky Spin” game. In the game, the customer spins the first wheel (which is divided into $3$ equal parts) to see how much money he wins, then he spins a second wheel to see how much his winning is multiplied by.

For example, based on the illustration above, if the result from the first spin is “$\$10$”, and the result of the second spin is“$\times 4$”, then the person playing the game would have received $\$40$. 

Let $X$ denote the amount won from playing the game.

Tabulate the probability distribution of $X$.

ABC Supermart makes a profit of $40$% on all purchases made by customers. It wishes to use the profits generated from every qualifying receipt to offset the amounts given away in the game. Determine the value of $\${}R$ that the Supermart needs to set for a customer to qualify to play the game. Give your answer correct to the nearest dollar.

Find the value of $\sigma$, the standard deviation of $X$. Hence find $\mathrm{P}\left( X<\sigma \right)$.

2019 CJC P2 Q6

2019 CJC P2 Q6

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