Construct the confidence interval for the population mean μ. c=0.99, xˉ=5.4, σ=1.2, and n=60. A 99% confidence interval for μ is ___ , ___. (Round to two decimal places as needed.)

Answer:
Given:
Sample mean $(\bar{x}) = 5.4$

Population standard deviation $(\sigma) = 1.2$

Sample size $(n) = 60$

Confidence interval level $= 99\%$

Solution:
The significance level $(\alpha):$
$\therefore (\alpha) = 1 – 0.99 = 0.01$

The critical value $(z_c):$
The critical value at 0.01 significance level $= 2.58$

The confidence interval:
$CI = \bar{x} \pm z_c \cdot \frac{\sigma}{\sqrt{n}} = 5.4 \pm 2.58 \cdot \frac{1.2}{\sqrt{60}} = (5.013, 5.787) \approx (5.01, 5.79)$

Final answer:
The 99\% confidence interval $= (5.01, 5.79)$