SOLUTION: A soda machine dispenses soda into 16-ounce cups. Tests shows that the actual amount of soda dispensed has a mean of 15.85 oz and a standard deviation of 9.5 oz. A sample of 12 cup

Question 1192785: A soda machine dispenses soda into 16-ounce cups. Tests shows that the actual amount of soda dispensed has a mean of 15.85 oz and a standard deviation of 9.5 oz. A sample of 12 cups is taken. What is the probability that the sample mean is between 14.75 and 22.5?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
z=(x-mean)/sigma/sqrt(n)
z=(14.75-15.85)/9.5/sqrt(12)=-1.10*sqrt(12)/9.5=-0.40
z=(22.5-15.85)/9.5/sqrt(12)=2.42
that probability is 0.6477.
The sd of the sample mean is 9.5/sqrt(12)=2.74
There is rounding of the z value above. If done on the calculator without rounding, the probability is 0.6481.
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