2.
At a toy factory, wooden blocks of approximate heights \(20 \mathrm {~mm} , 30 \mathrm {~mm}\) and 50 mm are made in red, yellow and green respectively. The heights of the blocks in mm are modelled by independent random variables which are Normally distributed with means and standard deviations as shown in the table.
| Colour | Mean | Standard deviation |
| Red | 20 | 0.8 |
| Yellow | 30 | 0.9 |
| Green | 50 | 1.2 |
In parts (a), (b) and (c), the blocks are selected randomly and independently of one another.
- Find the probability that the height of a red block is less than 19 mm .
- A tower is made of 15 blocks stacked on top of each other consisting of 5 red blocks, 5 yellow blocks and 5 green blocks.
Determine the probability that the tower is at least 495 mm high.
- Determine the probability that a tower made of 3 red blocks will be at least 1 mm higher than a tower made of 2 yellow blocks.
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