At a work station, $$5$$ jobs arrive every minute. The mean time spent on each job in the work station is $$1/8$$ minute. The mean steady state number of jobs in the system is __________

Demand during lead time with associated probabilities is shown below:

Expected demand during lead time is ___________

A bolt of major diameter $$12$$ $$mm$$ is required to clamp two steel plates. Cross sectional area of the threaded portion of the bolt is $$84.3$$ $$m{m^2}$$ . The length of the threaded portion in grip is $$30$$ $$mm,$$ while the length of the unthreaded portion in grip is $$8$$ $$mm.$$ Young's modulus of material is $$200$$ $$GPa.$$ The effective stiffness (in $$MN/m$$) of the bolt in the clamped zone is _______.

A shaft is subjected to pure torsional moment. The maximum shear stress developed in the shaft is $$100$$ $$MPa.$$ The yield and ultimate strengths of the shaft material in tension are $$300$$ $$MPa$$ and $$450$$ $$MPa,$$ respectively. The factor of safety using maximum distortion energy (Von - Mises) theory is __________.