7. Flaws occur at random in a particular type of material at a mean rate of 2 per 50 m .
- Find the probability that in a randomly chosen 50 m length of this material there will be exactly 5 flaws.
This material is sold in rolls of length 200 m . Susie buys 4 rolls of this material.
- Find the probability that only one of these rolls will have fewer than 7 flaws.
A piece of this material of length \(x \mathrm {~m}\) is produced.
Using a normal approximation, the probability that this piece of material contains fewer than 26 flaws is 0.5398
- Find the value of \(x\).