4. Strips of metal are cut to length \(L \mathrm {~cm}\), where \(L \sim \mathrm {~N} \left( \mu , 0.5 ^ { 2 } \right)\).
- Given that \(2.5 \%\) of the cut lengths exceed 50.98 cm , show that \(\mu = 50\).
- Find \(\mathrm { P } ( 49.25 < L < 50.75 )\).
Those strips with length either less than 49.25 cm or greater than 50.75 cm cannot be used.
Two strips of metal are selected at random. - Find the probability that both strips cannot be used.