A manufacturer of industrial solvent guarantees its customers that each drum of

Q: A manufacturer of industrial solvent guarantees its customers that each drum of

a) hence probability that a drum meets the guarantee b) here for 99% relaibility at 1st th percentile ; critical z = -2.3263 hence corresponding std deviation =(X-mean)/z score =-(100-103.3)/2.3263 =1.419 (please try 1.416 if this does not work due to rounding) for normal distribution z score =(X-)/ here mean= = 103.300 std deviation == 3.93

ID: 3047748 • Letter: A

Question

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 103.3 pounds and a standard deviation of 3.93 pounds.

a) What is the probability that a drum meets the guarantee? Give your answer to four decimal places. 1

b) What would the standard deviation need to be so that the probability a drum meets the guarantee is 0.99? Give your answer to three decimal places. 2

Explanation / Answer

hence probability that a drum meets the guarantee

here for 99% relaibility at 1st th percentile ; critical z = -2.3263

hence corresponding std deviation =(X-mean)/z score =-(100-103.3)/2.3263 =1.419 (please try 1.416 if this does not work due to rounding)

for normal distribution z score =(X-)/ here mean= = 103.300 std deviation == 3.93

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A manufacturer of industrial solvent guarantees its customers that each drum of

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A manufacturer of industrial solvent guarantees its customers that each drum of

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