Final answer:
To find the mean diameter and standard deviation for the sample, use the formulas for the mean and standard deviation of a sample. To find the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches, use the z-score formula and the standard normal distribution table.
Step-by-step explanation:
To find the mean diameter and standard deviation for the sample, we can use the formulas for the mean and standard deviation of a sample. The mean diameter of the sample is the same as the population mean, which is 208 inches. The standard deviation of the sample can be found using the formula:
Standard Deviation of Sample = Population Standard Deviation / Square Root of Sample Size
So, the standard deviation of the sample is 1.3 / √60 ≈ 0.168 inches.
To find the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches, we can use the z-score formula and the standard normal distribution table. The z-score formula is:
Z = (Sample Mean - Population Mean) / (Population Standard Deviation / Square Root of Sample Size)
Using this formula, we can calculate the z-score and find the probability using the standard normal distribution table.