To calculate the minimum sample size required to provide a 95% confidence interval for a mean with a maximum margin of error of 1.25 cm, we can use the formula:
n = (Z * σ / E)^2
Where:
n = required sample size
Z = Z-score corresponding to the desired confidence level (for a 95% confidence level, Z ≈ 1.96)
σ = standard deviation of the population
E = maximum margin of error
Plugging in the values:
Z ≈ 1.96
σ = 4 cm
E = 1.25 cm
n = (1.96 * 4 / 1.25)^2
n ≈ 48.89
Therefore, the minimum sample size required to provide a 95% confidence interval with a maximum margin of error of 1.25 cm is approximately 49. Keep in mind that since the sample size must be a whole number, you would need to round up to the nearest integer.