Final answer:
To estimate the idle time, divide the number of idle observations (8) by the total (50) and multiply by 100 to get 16%. The sample size needed for a 99% confidence interval and a margin of error of 7% requires a calculation with the Z-score, which is not provided in this summary.
Step-by-step explanation:
The student's question is regarding the estimation of idle time for air-express cargo loaders based on initial observations and determining the sample size required for a specific confidence interval and margin of error.
a. Estimated percentage of idle time
The estimated percentage of idle time can be calculated by dividing the number of observations where loaders were idle by the total number of observations and then multiplying by 100. In this case, 8 idle observations out of 50 gives an estimated idle time percentage of (8/50)*100 = 16%.
b. Sample size for confidence interval
To calculate the required sample size to estimate the actual percentage of idle time within a certain margin of error at a given confidence level, a formula involving the estimated proportion, the desired margin of error, and the Z-score for the confidence level must be used. For a 99% confidence level, the Z-score is typically about 2.576. However, without performing the actual calculation, it's not possible to provide the exact sample size needed.