SOLUTION: Cans of classic Coke are filled so that the mean is 12.0 ounces with a standard deviation of 0.1 ounces. Find the probability that a) a single can will have 12.2 or more ounces

Question 581393: Cans of classic Coke are filled so that the mean is 12.0 ounces with a standard deviation of 0.1 ounces. Find the probability that
a) a single can will have 12.2 or more ounces
b) a sample of 36 cans will have 12.2 or more ounces
c) Explain the difference in the answers for parts a and b
Any help would be awesome.
Thank you
Rae
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Cans of classic Coke are filled so that the mean is 12.0 ounces with a standard deviation of 0.1 ounces. Find the probability that
a) a single can will have 12.2 or more ounces
z(12.2) = (12.2-12)/0.1 = 0.2/0.1 = 2
P(x >= 12.2) = P(z >= 2) = normalcdf(2,100) = 0.0228
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b) a sample of 36 cans will have 12.2 or more ounces
z(12.2) = (12.2-12)/[0.1/sqrt(36)] = 0.2/(0.1/6) = 12
P(x-bar >= 12.2) = P(z >= 12) = normalcdf(12,100) = 1.831 x 10^-33
----------------------------------------------------------
c) Explain the difference in the answers for parts a and b
The standard deviation for all sample means of size 36 is
much, much, much smaller than the standard deviation for the
population. Therefore the z-value for the sample means
is much larger and the probability of z being greater is smaller.
Cheers,
Stan H.
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