A machine that is programmed to package 5.69 pounds of cereal is being tested for its accuracy. In a sample of 100 cereal boxes, the sample mean filling weight is calculated as 5.69 pounds. The population standard deviation is known to be 0.05 pound. Use Table 1. 
a1. 
Identify the relevant parameter of interest for these quantitative data. 


a2. 
Compute its point estimate as well as the margin of error with 99% confidence. (Round intermediate calculations to 4 decimal places. Round "zvalue" to 3 decimal places and final answers to 2 decimal places.) 
Point estimate  
Margin of error  
b1. 
Calculate the 99% confidence interval. (Use rounded margin of error. Round your final answers to 2 decimal places.) 
Confidence interval  to 
b2. 
Can we conclude that the packaging machine is operating improperly? 


c. 
How large a sample must we take if we want the margin of error to be at most 0.01 pound with 99% confidence? (Round intermediate calculations to 4 decimal places. Round "zvalue" to 3 decimal places and round up your final answer to the next whole number.) 
Sample size 
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