Answer:
The 95% confidence interval is [tex](150\pm 8.8)[/tex].
Step-by-step explanation:
The information provided is:
[tex]\bar x=150\\\sigma = 20\\n=20[/tex]
The critical value for 95% confidence level is:
[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96[/tex]
Compute the margin of error as follows:
[tex]MOE=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}[/tex]
[tex]=1.96\times\frac{20}{\sqrt{20}}\\\\=1.96\times 4.47214\\\\=8.7653944\\\\\approx 8.8[/tex]
Then the 95% confidence interval is:
[tex]CI=\bar x\pm MOE[/tex]
[tex]=150\pm 8.8[/tex]
Thus, the 95% confidence interval is [tex](150\pm 8.8)[/tex].
