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

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 102.9 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.  

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.

Explanation / Answer

answer of a)

here we go for z-test

z=x--mu/sigma

here x-=100,mu=102.9,sigma=3.93

z=(100-102.9)/3.93=-0.7379

we want

p(z>-0.7379)=1-0.2302=0.7698

answer b)

p(z>z1)=0.97 this imply z1=1.88

|(100-102.9)|/sigma=1.88

sigma=2.9/1.88=1.54

standard deviation should be 1.54

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