Provide an appropriate response.
-Construct a $95 \%$ confidence interval for the population mean, $\mu$. Assume the population has a normal distribution. A random sample of 16 lithium batteries has a mean life of 645 hours with a standard deviation of 31 hours.
A) $( 628.5,661.5 )$
B) $( 876.2,981.5 )$
C) $( 531.2,612.9 )$
D) $( 321.7,365.8 )$

Question

Quizplus · Accepted Answer

To construct a 95% confidence interval for the population mean, we use the formula: $\bar{x} \pm z\frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $z$ is the z-score corresponding to the confidence level (for 95%, $z = 1.96$), $\sigma$ is the standard deviation, and $n$ is the sample size. Plugging in the given values: $645 \pm 1.96\frac{31}{\sqrt{16}}$ results in the interval $(628.5, 661.5)$.

Provide an Appropriate Response 95%95 \%95% Confidence Interval for the Population Mean

Provide an Appropriate Response $95 \%$ Confidence Interval for the Population Mean