Bearco produces alutin (and alloy of aluminium and tin) bearings for truck engines. prior to shaping, ingots
of alutin pass through a rolling mill, where they are reduced to a mean thickness of 3.05 mm , with a
standard deviation of 0.025 mm.
the alutin ingots can be shaped if their thickness is between 2.97 mm and 3.08 mm. these ingots are
described as “in spec”. if they are outside that range they are “out of spec” and need to be melted down and
recast.
a) assuming that alutin ingot thickness follows a normal distribution, determine the probability that
a randomly selected ingot is suitable to be shaped.
b) bearco needs 48 ingots for a bearing production run. if they roll 50 ingots, determine the
probability that they will have enough “in spec” ingots for the production run. identify any
assumptions you need to make.
c) (*) if bearco need 300 “in spec” ingots for a production run, determine the minimum number
that should rolled, such that there is at least a 95% probability that they will have enough.