Question

A random sample of 56 lithium batteries has a mean life of 645 hours with a population standard deviation of 31 hours. Compute the​ 95% confidence interval for mu. A. ​(636.9, 653.1) B. ​(712.0, 768.0) C. ​(539.6, 551.2) D. ​(112.0, 118.9)

Answer 1

Answer: A. ​(636.9, 653.1)

Explanation:

Given : Sample size : n=56

Significance level :
`\alpha: 1-0.95=0.05`

Critical value :
`z_(0.05)=1.96`

Sample mean :
`\overline{x}=645\text{ hours}`

Standard deviation :
`\sigma= 31\text{ hours}`

The 95% confidence interval for population mean is given by :-

`\overline{x}\pm z_(\alpha/2)(\sigma)/(√(n))\\\\=645\pm (1.96)(31)/(√(56))\\\\=645\pm8.1\\\\=(636.9, 653.1)`

Hence, 95% confidence interval for population mean is (636.9, 653.1).