Final answer:
To find the probability that the mean length of a sample of 41 boards is greater than 98.17 inches, we need more information about the standard deviation and sample mean.
Step-by-step explanation:
To find the probability that the mean length of a sample of 41 boards is greater than 98.17 inches, we need to use the central limit theorem. The central limit theorem states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases. We can use the standard normal distribution to calculate probabilities.
First, we calculate the standard error of the mean (SE) using the formula:
SE = standard deviation / sqrt(sample size)
Given the information in the question, we have:
Standard deviation = ? (not given)
Sample size = 41
Next, we calculate the z-score using the formula:
z = (sample mean - population mean) / SE
Given the sample mean and population mean are not given, we cannot calculate the z-score and determine the probability. We need more information to accurately solve the problem.