Choose the one alternative that best completes the statement or answers the 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) $( 539.6,551.2 )$
C) $( 112.0,118.9 )$
D) $( 712.0,768.0 )$

Question

Quizplus · Accepted Answer

The $95\%$ confidence interval for the mean $\mu$ can be calculated using the formula for the confidence interval when the population standard deviation is known: $\bar{x} \pm Z \frac{\sigma}{\sqrt{n}}$, 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 population standard deviation, and $n$ is the sample size. Plugging in the given values: $645 \pm 1.96 \frac{31}{\sqrt{56}}$, we get the interval $(636.9, 653.1)$.

Choose the One Alternative That Best Completes the Statement or Answers