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## Sagot :

**Answer:**

**98% confidence interval for the population mean =(1095.260,1288.740)**

**Step-by-step explanation:**

We are given that

n=45

[tex]\mu=1192[/tex]

Standard deviation,[tex]\sigma=279[/tex]

We have to construct a 98% confidence interval for the population mean.

Critical value of z at 98% confidence, Z =2.326

Confidence interval is given by

[tex](\mu\pm Z\frac{\sigma}{\sqrt{n}})[/tex]

Using the formula

98% confidence interval is given by

[tex]=(1192\pm 2.326\times \frac{279}{\sqrt{45}})[/tex]

[tex]=(1192\pm 96.740)[/tex]

=[tex](1192-96.740,1192+96.740)[/tex]

**=**[tex](1095.260,1288.740)[/tex]

**Hence, 98% confidence interval for the population mean (1095.260,1288.740)**