The quantity of liquid medication that is dispensed by a machine has a normal distribution with...
The quantity of liquid medication that is dispensed by a machine has a normal distribution with mean µ ml (which can be set by the hospital) and standard deviation 0.75 ml. Suppose that the machine is being used by the hospital to fill 150.00 ml vials.
a. If the hospital sets µ equal to 150.00 ml, what proportion of the time will the machine overfill the vial? (4 decimals)
b. If the hospital sets µ equal to 149.50 ml, what proportion of the time will the machine overfill the vial? (4 decimals)
c. If the hospital wishes to have the machine overfill the vial only 3% of the time, at what value of µ should the machine be set? (2 decimals)
d. The hospital would like to acquire a more precise
machine, such that the quantity of liquid dispensed has a smaller
standard deviation σ. They would like to be able to set the new
machine at µ = 149.50 ml, and have the 150.00 ml vials overfill
only 3% of the time. How small does the standard deviation σ for
the new machine have to be? (3 decimals)
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