Iron plates are required to have a certain thickness but each plate produced will differ slightly from each other due to properties of the material and uncertainties in the behaviour of the machines that make them. Let X be the plate thickness in mm of plates produced by a given machine. Using the machine's default setting, X follows a normal distribution with mean 10mm and standard deviation 0.02mm (a) What percentage of plates should be expected to be thinner than 0.97mm? (b) What percentage of plates should be expected to be thicker than 10:05mm? (c) What percentage of p
Iron plates are required to have a certain thickness but each plate produced will differ slightly
from each other due to properties of the material and uncertainties in the behaviour of the machines
that make them. Let X be the plate thickness in mm of plates produced by a given machine. Using
the machine's default setting, X follows a
deviation 0.02mm
(a) What percentage of plates should be expected to be thinner than 0.97mm?
(b) What percentage of plates should be expected to be thicker than 10:05mm?
(c) What percentage of plates should be expected to deviate in thickness by more than 0.03mm
from 10.00mm?
(d) Find c > 0 to ensure that 5% of plates are expected to deviate in thickness by more than c
mm from 10.00mm?
(e) Given the c found in part (d), what percentage of plates are expected to deviate by more than
c mm from 10.00mm if a slight adjustment in the machine shifts the
10.01mm
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