Answer:
95% Confidence Interval: (94.08,101.92)
Step-by-step explanation:
We are given the following in the question:
Sample mean, [tex]\bar{x}[/tex] = 98
Sample size, n = 36
Alpha, α = 0.05
Population standard deviation, σ = 12
95% Confidence Interval:
Formula:
[tex]\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}[/tex]
Putting the values, we get,
[tex]z_{critical}\text{ at}~\alpha_{0.05} = 1.96[/tex]
[tex]98 \pm 1.96(\dfrac{12}{\sqrt{36}} ) = 98 \pm 3.92 = (94.08,101.92)[/tex]
