A machine that is programmed to package 4.20pounds of cereal is being tested for its accuracy. In a sample of 36 cereal boxes, the sample mean filling weight is calculated as 4.23 pounds. The population standard deviation is known to be 0.12 pound.[You may find it useful to reference thez table.]

a-1.Identify the relevant parameter of interest for these quantitative data.

• The parameter of interest is the proportion filling weight of all cereal packages.
• The parameter of interest is the average filling weight of all cereal packages.

a-2.Compute its point estimate as well as the margin of error with 90% confidence.(Round intermediate calculations toat least 4 decimal places. Round "z" value to 3 decimal places and final answers to 2 decimal places.)

Point Estimate: ______

Margin of Error: ______

b-1.Calculate the 90% confidence interval.(Use rounded margin of error. Round your final answers to 2 decimal places.)

Confidence Interval: _______ to _______

b-2.Can we conclude that the packaging machine is operating improperly?

• Yes, since the confidence interval does not contain the target filling weight of 4.20.
• No, since the confidence interval contains the target filling weight of 4.20.
• Yes, since the confidence interval contains the target filling weight of 4.20.
• No, since the confidence interval does not contain the target filling weight of 4.20.

c.How large a sample must we take if we want the margin of error to be at most 0.02 pound with 90% confidence?(Round intermediate calculations toat least4 decimal places. Round "z" value to 3 decimal places and round up your final answer to the next whole number.)

Sample Size: ________