You are interested in estimating the the mean weight of the local adult population of female white-tailed deer (doe). From past data, you estimate that the standard deviation of all adult female white-tailed deer in this region to be 41 pounds. What sample size would you need to in order to estimate the mean weight of all feriale white-tailed deer, with a $98 \%$ confidence level, to within 8 pounds of the actual weight? (Use Excel to find the appropriate critical value and round to 3 decimal places.) Sample Size: Submit Question

Step 1 ：We are given that the standard deviation (σ) is 41 pounds, the margin of error (E) is 8 pounds, and the z-score (Z) for a 98% confidence level is approximately 2.33.

Step 2 ：We can use the formula for the sample size in a confidence interval estimation, which is: \(n = (Z*σ/E)^2\)

Step 3 ：Substitute the given values into the formula: \(n = (2.33*41/8)^2\)

Step 4 ：Calculate the value to get the sample size.

Step 5 ：\(\boxed{143}\) is the sample size needed to estimate the mean weight of all female white-tailed deer with a 98% confidence level, to within 8 pounds of the actual weight.