Final answer:
To find the 99% upper confidence bound for the mean wall thickness of steel canisters, calculate the upper limit using the sample mean, standard deviation, sample size, and the z-score corresponding to the 99% confidence level, which is 2.576.
Step-by-step explanation:
The question is asking for a 99% upper confidence bound for the mean wall thickness of a sample of steel canisters. In statistics, confidence intervals can be used to estimate parameters like the population mean. To calculate this upper confidence bound, one typically uses z-scores, which represent the number of standard deviations an element is from the mean. When the standard deviation is known, and the sample size is large (n ≥ 30), we use the standard normal distribution (z-distribution). The z-score corresponding to a 99% confidence level is approximately 2.576.
The upper confidence bound (UCB) is calculated using the formula:
UCB = μ + (z × (σ/√n)), where μ is the sample mean, σ is the standard deviation, and n is the sample size. Plugging in the values given, we get: UCB = 8.2mm + (2.576 × (0.4mm/√100)), which results in UCB = 8.2mm + (2.576 × 0.04mm). After performing the multiplication, we add this value to the sample mean to find the upper confidence bound.
The upper confidence bound for the mean wall thickness, at a 99% confidence level, helps us understand the maximum expected average thickness of the steel canisters, provided the sample data and assumptions are accurate. It's a useful measure for quality control and assurance processes in engineering and manufacturing industries.