A machine is used to manufacture 3-cm nails. The lengths of 3-cm nails are normally distributed with a mean of 3.0 cm and a standard deviation of 0.09 cm. The nails that are either shorter than 2.9 cm...

Extracted text: A machine is used to manufacture 3-cm nails. The lengths of 3-cm nails are normally distributed with a mean of 3.0 cm and a standard deviation of 0.09 cm. The nails that are either shorter than 2.9 cm or longer than 3.1 cm are unusable. (i) Find the percentage of all nails produced by this machine which are unusable. (ii) Find k such that 90% of the nails will have the length less than k cm. (iii) Calculate the probability that a random sample of 25 nails will have a total length of more than 76 cm.