A company produces metal support using an automatic machine of various lengths. engineering department specifications for the length of a particular bracket are between 12mm and 100mm It is the supports produced by the automatic machine without outside these standards They will cause significant assembly difficulties

a) assuming that the length of the supports is normally distributed what is the standard deviation of the length of the supports that is actually specified in the service it is assumed that the service corresponds to 99.74% of the production

b) Assuming that the automatic machine produces supports conforming to the specified standards how many of a production of 8000 supports will probably have a length less than 94 mm

C) The machine is automatic and in operation and we want to check if it is set correctly, i.e. adjusted to obtain supports of 100 mm in length on average. A random sample of 18 supports gives an average length of 102 mm . would this result lead us to believe that the machine is adjusted incorrectly? it is assumed that you limit to 1% the risk of stopping the machine unnecessarily to change the adjustment it is assumed variance = 16

d) Assuming that the automatic machine is correctly adjusted, what are the chances of observing for a sample of size n=18 an average length greater than or equal to 101 mm, we assume variance =16