- A machine cuts strips of metal to length \(L \mathrm {~cm}\), where \(L\) is normally distributed with standard deviation 0.5 cm .
Strips with length either less than 49 cm or greater than 50.75 cm cannot be used.
Given that 2.5\% of the cut lengths exceed 50.98 cm ,
- find the probability that a randomly chosen strip of metal can be used.
Ten strips of metal are selected at random.
- Find the probability fewer than 4 of these strips cannot be used.
A second machine cuts strips of metal of length \(X \mathrm {~cm}\), where \(X\) is normally distributed with standard deviation 0.6 cm
A random sample of 15 strips cut by this second machine was found to have a mean length of 50.4 cm
- Stating your hypotheses clearly and using a \(1 \%\) level of significance, test whether or not the mean length of all the strips, cut by the second machine, is greater than 50.1 cm