At a bottling plant, two machines are used to ll 500 ml bottles of pop. The amou

Question

At a bottling plant, two machines are used to ll 500 ml bottles of pop. The amount of pop put into each bottle by Machine A is a normal random variable with a mean of 508ml and

a standard deviation of 5ml. Similarly, amount of pop put into each bottle by by Machine B is a normal random variable with a mean of 506ml and a standard deviation of 4ml. If

Machine A is used to ll 60% of bottles.

(a) What percentage of bottles containing less than 499ml comes from Machine B

Can anyone explain this to me ? The correct answer is 42.68 % Thanks !

Explanation / Answer

Let the total number of bottles be 100

Machine A =60

Machine B =40

Z value such that bottle hav vol<499ml from machine A

= 499-508 / 5 = -1.8

=35.93% ==>60*0.3593=21.558 bottles

Z value such that bottle hav vol<499ml from machine B

= 499-506 / 4 = -1.75=40.06%==>40*0.4006=16.024

So % bottles containing less than 499ml coming from Machine B=[16.024/(21.558+16.024) ]*100=42.64%

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