Answer:
a) (59180,60820)
b) (59020,60980)
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = $60,000
Standard Deviation, σ = $5,000
Sample size, n = 100
a) 90% critical values
[tex]\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}[/tex]
Putting the values, we get,
[tex]z_{critical}\text{ at}~\alpha_{0.10} = 1.64[/tex]
[tex]60000 \pm 1.64(\frac{5000}{\sqrt{100}} ) = 60000 \pm 820 = (59180,60820)[/tex]
b) 95% critical values
[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]60000 \pm 1.96(\frac{5000}{\sqrt{100}} ) = 60000 \pm 980= (59020,60980)[/tex]
