2025 ASRJC P2 Q9
2025 ASRJC P2 Q9
In this question, you should state clearly all the distributions that you use, together with the values of the appropriate parameters.
A toy designer creates weighted wooden blocks used in balance-based educational toys. There are two types of blocks: cylindrical blocks and cuboidal blocks. The mass, in grams, of each cylindrical block and cuboidal block follow a normal distribution with the following parameters:
| Mean | Standard Deviation | |
|---|---|---|
| cylindrical block | \(280\) | \(6\) |
| cuboidal block | \(220\) | \(5\) |
- Find the probability that the mass of a randomly selected cylindrical block exceeds the mass of a randomly selected cuboidal block by more than \(65\) grams.[2]
- The probability that the total of twice the mass of a cylindrical block and thrice the mass of a cuboidal block being less than \(M\) g is \(0.355\). Find the value of \(M\), giving your answer to the nearest integer.[2]
To build a deluxe seesaw model, the designer uses:
- \(2\) cylindrical blocks,
- \(3\) cuboidal blocks,
- \(7\) screws,
- \(1\) wooden plank.
The blocks are drilled before assembly to fit screws:
- Each cylindrical block loses \(5\)% of its mass after drilling.
- Each cuboidal block loses \(3\)% of its mass after drilling.
The masses of the remaining components follow a normal distribution with the following parameters:
| Mean | Standard Deviation | |
|---|---|---|
| screw | \(8\) | \(1.2\) |
| wooden plank | \(540\) | \(8\) |
When assembling the deluxe seesaw model, all of its components are chosen at random.
- Find the probability that the total mass of all the modified components in a deluxe seesaw model is more than \(1785\) g.[4]
Solution:
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(a) \(0.261\).
(b) \(M=1213\) g, to the nearest integer.
(c) \(0.123\).
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