With known σ = 15, n = 25, and x̄ = 100, which is the correct 95% confidence interval for μ?

• A. [94.12, 105.88]
• B. [95.00, 105.00]
• C. [90.00, 110.00]
• D. [94.00, 106.00]

Answer: (A)

The main idea is that when the population standard deviation is known, you use a Z-based confidence interval: x̄ ± z_{0.025} * (σ/√n). Here, x̄ = 100, σ = 15, n = 25, so σ/√n = 15/√25 = 3. The 95% critical value is 1.96, giving a margin of error of 1.96 × 3 = 5.88. So the interval is 100 ± 5.88, which is [94.12, 105.88]. This is the correct interval because it uses the known σ in the standard error and the correct 95% z multiplier. The other options would arise from using a different margin of error or a different distribution (for example, a wider interval if a t-distribution were used with unknown σ), so they don’t fit the given data.