- A shop sells rods of nominal length 200 cm . The rods are bought from a manufacturer who uses a machine to cut rods of length \(L \mathrm {~cm}\), where \(L \sim \mathrm {~N} \left( \mu , 0.2 ^ { 2 } \right)\)
The value of \(\mu\) is such that there is only a \(5 \%\) chance that a rod, selected at random from those supplied to the shop, will have length less than 200 cm .
- Find the value of \(\mu\) to one decimal place.
A customer buys a random sample of 8 of these rods.
- Find the probability that at least 3 of these rods will have length less than 200 cm .
Another customer buys a random sample of 60 of these rods.
- Using a suitable approximation, find the probability that more than 5 of these rods will have length less than 200 cm .