Find the confidence interval specified.
-A random sample of 110 light bulbs had a mean life of $\bar { x } = 595$ hours. Assume that $\sigma = 31$ hours. Construct a $90 \%$ confidence interval for the mean life, $\mu$, of all light bulbs of this type.
A)$590.1$ to $599.9$ hours
B) $587.4$ to $602.6$ hours
C) $588.1$ to $601.9$ hours
D) $589.2$ to $600.8$ hours

Question

Find the confidence interval specified.
-A random sample of 110 light bulbs had a mean life of $\bar { x } = 595$ hours. Assume that $\sigma = 31$ hours. Construct a $90 \%$ confidence interval for the mean life, $\mu$, of all light bulbs of this type.  
A)$590.1$ to $599.9$ hours
B) $587.4$ to $602.6$ hours
C) $588.1$ to $601.9$ hours
D) $589.2$ to $600.8$ hours

Quizplus · Accepted Answer

The confidence interval is calculated using 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, $\sigma$ is the population standard deviation, and $n$ is the sample size. For a 90% confidence level, the Z-score is approximately 1.645. Plugging in the given values: $595 \pm 1.645 \frac{31}{\sqrt{110}}$ results in the interval $590.1$ to $599.9$.

Find the Confidence Interval Specified xˉ=595\bar { x } = 595xˉ=595

Find the Confidence Interval Specified $\bar { x } = 595$