The volume of soft drink that a dispensing machine pours into a 12 ounce can fol
ID: 3051798 • Letter: T
Question
The volume of soft drink that a dispensing machine pours into a 12 ounce can follows a
normal distribution with a mean of 12.48 ounces and a standard deviation of 0.32 ounce.
(a) The cans only hold 13 ounces of liquid. Every can that has more than 13 ounces of soft
drink poured into it causes a spill and the can must go through a special cleaning process
before it can be sold. What is the probability a randomly selected can will need to go
through this process?
(b) What volume is exceeded by 90% of the cans filled by the dispensing machine?
(c) What is the probability that the mean volume of soda per can in a six-pack is more than
12.5 ounces?
(d) What is the probability that the total volume of soda in a six-pack is more than 75
ounces?
Explanation / Answer
a)
probability a randomly selected can will need to go through this process:
b)
for 10th percentile ; critical z =-1.2816
hence corresponding value =mean +z*std deviation =12.48-1.2816*0.32 =12.4151
c)
d) for expected total volume =12.48*6=74.88
std deviation =0.32*(6)1/2 =0.7838
for normal distribution z score =(X-)/ here mean= = 12.480 std deviation == 0.32Related Questions
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