Each can is supposed to consist of precisely 15 grams of aluminum, and the marke

Question

Each can is supposed to consist of precisely 15 grams of aluminum, and the market price for aluminum is $0.95 per pound (important note: there are 454 grams in one pound). Sample of 100 cans
The Akron plant produces 2 billion cans every year.

Data
Sample Standard Deviation 0.98
Sample Mean 15.94
Sample Size 100
Confidence Level 95%

Intermediate Calculations
Standard Error of the Mean 0.0981
Degrees of Freedom 99
t Value 1.9842
Interval Half Width 0.1947

Confidence Interval
Interval Lower Limit 15.74
Interval Upper Limit 16.13

-Construct a 95% confidence interval for the total expenditure on aluminum at the Akron plant. How much money could AluminiCorp save if the Akron plant actually produced cans that were at the target aluminum content?

Explanation / Answer

Given xbar=15.94, s=0.98, n=100
a=0.05, Z(0.025)=1.96(check standard normal table)

So 95% CI is
xbar ± Z*s/n

--> 15.94 ± 1.96*0.98/10

--> ( 15.748, 16.132)

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