solution to homework 7

solution to homework 7 - Statistics V3100018.001-006...

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Statistics – V3100018.001-006 Solutions to homework 7 Giuseppe Arbia , Catholic University of the Sacred Hearth, Roma, Italy 1
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Ques%on 1 A brewery has a beer dispensing machine that pours beer into the company’s 12 ounce bo8les. The distribu<on of the amount of beer actually dispensed by the machine follows a Normal distribu<on with a standard devia<on of 0.2 ounces. The company can control the mean amount of beer dispensed by the machine. (a) What value of the mean should the company set if it wants to guarantee that 98.5% of the bo8les contain at least 12 ounces (the amount on the label)? (b) Suppose now that the distribu<on of pours is Normal with mean 12.1 and standard devia<on 0.5. Customers get very angry when their beers have less than the adver<sed 12 ounces of beer in them. Calculate the propor<on of customers that could get angry because of this reason .
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X ! N ( μ ; ! = 0.2) P ( X > x ) = 0.985 P ( X < x ) = 1 ! 0.985 = 0.015 P Z < x ! μ ! = z 0.015 " # $ % & = 0.015
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‐2.17
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z 0.015 = ! 2.17 x ! μ !
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