4. Pieces of ribbon are cut to length \(L \mathrm {~cm}\) where \(L \sim \mathrm {~N} \left( \mu , 0.5 ^ { 2 } \right)\)
- Given that \(30 \%\) of the pieces of ribbon have length more than 100 cm , find the value of \(\mu\) to the nearest 0.1 cm .
John selects 12 pieces of ribbon at random.
- Find the probability that fewer than 3 of these pieces of ribbon have length more than 100 cm .
Aditi selects 400 pieces of ribbon at random.
- Using a suitable approximation, find the probability that more than 127 of these pieces of ribbon will have length more than 100 cm .