The volume of soda a dispensing machine pours into a 12-ounce can of soda follow
ID: 3364225 • Letter: T
Question
The volume of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.03 ounces and a standard deviation of 0.02 ounce. The company receives complaints from consumers who actually measure the amount of soda in the cans and claim that the volume is less than the advertised 12 ounces.
a) What is the percentage of the soda cans contain less than the advertised 12 ounces of soda?
b) What is the percentage of the soda cans contain between 12 and 12.06 ounces of soda?
Explanation / Answer
P(X < A) = P(Z < A - mean)/standard deviation)
Mean = 12.03 ounce
Standard deviation = 0.02 ounce
a) P(X < 12 ounces) = P(Z < (12 - 12.03)/0.02)
= P(Z < -1.5)
= 0.0668
= 6.88%
b) P(12 < X < 12.06)
= P(X < 12.06) - P(X < 12)
= P(Z < (12.06 - 12.03)/0.02) - P(Z < (12 - 12.03)/0.02)
= P(Z < 1.5) - P(Z < -1.5)
= 0.9332 - 0.0668
= 0.8664
Percentage of soda cans containing between 12 and 12.06 ounces of soda = 86.64%
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