problem 28

Starting from the fact given in the problem

P (| Y - μ | < 1.96 σ) \approx 0.95

P (- 1.96 σ < Y - μ < 1.96 σ) \approx 0.95

P (Y - 1.96 σ < μ < Y + 1.96 σ) \approx 0.95

P (μ \in (Y - 1.96 σ, Y + 1.96 σ)) \approx 0.95

Therefore, the random interval that contains $μ$ about 95% of the time is $(Y - 1.96 σ, Y + 1.96 σ)$ .