The Almak company produces, using an automatic machine, metal supports of various lengths. The length of cut can be obtained using an adjustment of the machine. Media made by this machine are used in another department for the assembly of a certain product. However, the length of the supports must meet certain standards for a significant component of the final product can be assembled correctly. The engineering department's specifications for the length of a particular bracket are 100mm 12mm. If the media produced by the automatic machine is in outside these standards (too small or too long), they will cause assembly difficulties important, which can even cause the assembly line to stop. (Note: Subquestions a), b), d) can be done without using Excel) a) Assuming that the length of the supports is normally distributed, what is the standard deviation of the length of the supports which is actually specified in the specifications? It is assumed that the specifications correspond to 99.74% of the production. b) Assuming that the automatic machine produces media that conforms to the specified standards, how many, out of a production of 8000 supports, will have probably a length less than 94 mm? (2 points) c) The automatic machine is in operation and we want to check if it is set correctly i.e. adjusted to obtain, on average, supports of 100 mm length. A random sample of 18 supports gives an average length 102mm. Would this result lead us to believe that the machine is adjusted incorrectly? We will assume that you limit the risk of quitting unnecessarily to 1%. the automatic machine to change the fit. We assume ?2 = 16 d) Assuming that the automatic machine is set correctly, what are the chances out of 100 of observing, for a sample of size n = 18, a length average greater than or equal to 101 mm? We assume ?2 = 16 e) With a sample of this size and the level of significance specified in c), what is the risk of concluding that the machine is adjusted correctly, when it would be actually centered at 98 mm? We assume ?2 = 16 f) We also want to check if the dispersion of the length of the supports seems meets specifications. For the sample in c), we get