SOLUTION: 3. Cans of regular Coke are labeled as containing 12.00 oz. Assume that the actual contents are normally distributed with a mean of 12.19 oz and a standard deviation of 0.11 oz.

Question 357946: 3. Cans of regular Coke are labeled as containing 12.00 oz. Assume that the actual contents are normally distributed with a mean of 12.19 oz and a standard deviation of 0.11 oz.
a. What percentage of cans contain less than 12.10 oz ?

b. What amount of Coke separates the top 10% of the cans from the others?

c. To save some of the Coke in cans that are filled too much, the quality-control manager is instituting a plan to remove some of the Coke from cans that are in
the top 2%. What is the minimum amount of Coke in such cans that will be �reworked�?

d. What is the maximum amount of Coke in the cans that are in the bottom 15% ?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Cans of regular Coke are labeled as containing 12.00 oz. Assume that the actual contents are normally distributed with a mean of 12.19 oz and a standard deviation of 0.11 oz.
a. What percentage of cans contain less than 12.10 oz ?
---
z(12.10) = (12.10-12.19)/0.11 = -0.8182
---
P(x<12.10) = P(z< -0.8182) = 0.2066
=============================================
b. What amount of Coke separates the top 10% of the cans from the others?
Find the z with a right tail of 10%: z = 1.2816
----
x = 1.2816*0.11+12.19 = 12.33 ounces
=============================================
c. To save some of the Coke in cans that are filled too much, the quality-control manager is instituting a plan to remove some of the Coke from cans that are in the top 2%.
What is the minimum amount of Coke in such cans that will be �reworked�?
Find the z-value that has a 2% right tail.
invNorm(0.98) = 2.0537
---
x = 2.0537*0.11+12.19 = 12.42 ounces
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d. What is the maximum amount of Coke in the cans that are in the bottom 15% ?
Find the z with a left tail of 15%
invNorm(0.15) = -1.0364
x = -1.0364*0.11+12.19 = 12.0760
===================================
Cheers,
Stan H.

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