Estimate the Size of Random Samples of Eggs Laid by Hens

To estimate the mean mass of the eggs for this breed using a 90% confidence interval, we need to use the following formula: CI = X̄ ± Z * (σ / √n) where CI is the confidence interval, X̄ is the sample mean, Z is the Z-score associated with the desired confidence level, σ is the population standard deviation, and n is the sample size. We are given the following information: - X̄ = 57.2 grams (sample mean) - σ = 1.5 grams (standard deviation) - n = 200 (sample size) To find the Z-score associated with a 90% confidence interval, we should look at a Z-table. The Z-score for a 90% confidence interval is 1.645 (in a two-tailed test, alpha will be divided by 2, so actually we are looking for Z(0.95) on the table). Now, we can plug in the values into the formula: CI = 57.2 ± 1.645 * (1.5 / √200) CI = 57.2 ± 1.645 * (1.5 / 14.1421) CI = 57.2 ± 1.645 * 0.1061 CI = 57.2 ± 0.1746 So the 90% confidence interval is (57.0254, 57.3746). To the nearest tenth of a gram, we can estimate the mean mass of eggs for this breed to be between 57.0 grams and 57.4 grams.