A manufacturer of industrial solvent guarantees its customers
that each drum of solvent they ship out contains at least 100 lbs
of solvent. Suppose the amount of solvent in each drum is normally
distributed with a mean of 101.3 pounds and a standard deviation of
3.68 pounds.
a) What is the probability that a drum meets the guarantee? Give
your answer to four decimal places.
b) What would the standard deviation need to be so that the
probability a drum meets the guarantee is 0.97? Give your answer to
three decimal places.
a)
b)
Z score for 97 percentile is -1.881
= (100 -101.3)/-1.881 = 0.691
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