A Hepped Sampling of 200 Eggs Laid by Hens

To estimate the mean mass of the eggs for this breed using a 99% confidence interval, we will use the formula for the confidence interval of a mean with a known standard deviation: CI = x̄ ± (z * (σ / √n)) where: - CI is the confidence interval - x̄ is the sample mean (57.2 grams) - z is the z-score associated with the desired confidence level (99%) - σ is the known standard deviation (1.5 grams) - n is the sample size (200 eggs) First, we find the z-score for a 99% confidence interval. You can look up the z-score in a z-table, or use an online calculator. The z-value for a 99% confidence interval (which leaves 1% in the tails) is 2.576 (rounded to three decimal places). Now we can plug in the values into the formula: CI = 57.2 ± (2.576 * (1.5 / √200)) Now, calculate within the parentheses: CI = 57.2 ± (2.576 * (1.5 / 14.142)) CI = 57.2 ± (2.576 * 0.106) Now, multiply and add/subtract: CI = 57.2 ± 0.273 So, our 99% confidence interval for the mean mass of the eggs for this breed of hen is approximately (56.9, 57.5) grams, to the nearest tenth of a gram. This means we are 99% confident that the true mean mass of the eggs for this breed of hen falls within this interval.