2024 TMJC H1 Q12
2024 TMJC H1 Q12
13 marks
A quality control officer is checking on the assembly times for different types of electronic components in a factory. The assembly times, in minutes, for microchips and circuit boards follow independent normal distributions with given means and standard deviations as shown in the table.
| Mean | Standard deviation | |
|---|---|---|
| Microchips | \(45\) | \(7\) |
| Circuit Boards | \(75\) | \(10\) |
- It is known that \(85\)% of circuit boards take no more than \(t\) minutes to assemble. Find the value of \(t\).[2]
- Find the probability that the assembly time for a randomly chosen microchip takes more than \(50\) minutes.[1]
- Microchips are randomly chosen for inspection. Find the probability that the assembly time of the \(10^{\mathrm{th}}\) microchip is the \(2^{\mathrm{nd}}\) microchip that takes more than \(50\) minutes to assemble.[3]
- On a particular day, the factory needs to assemble \(6\) microchips and \(4\) circuit boards. Find the probability that the total assembly time for these randomly chosen components is less than \(500\) minutes.[3]
The factory charges \(\ 0.70\) per minute for the assembly of a circuit board.
- Find the probability that the total revenue from assembling \(6\) randomly chosen microchips and \(4\) randomly chosen circuit boards exceeds \$\(\ 350\).[4]
Solution:
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Answer:(i) \(85.4\) min; (ii) \(0.238\); (iii) \(0.0580\); (iv) \(0.00394\). (v) Underdetermined: microchip rate is missing. \(0.380\) is conditional on SGD 0.50/minute.
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