Let
μ = population mean
σ = population std. deviation.
n = sample size.
At 95% confidence level, the confidence interval is
(μ - 1.96y, μ + 1.96y),
where y = σ/√n.
Therefore
μ - 1.96y = 6.5 (1)
μ + 1.96y = 12.5 (2)
Add (1 and (2) to obtain
2μ = 19
μ = 9.5
The calculated value of μ is within the interval (6.5, 12.5).
Answer:
The statement "There is a 95% probability that the true population mean is between 6.5 and 12.5" is True.
