A random sample of electronic components had the following operational times before failure, in hours.

$\begin{array} { l l l l l }
\hline 322 & 350 & 346 & 347 & 335 \
\hline 323 & 341 & 355 & 329 & \
\hline
\end{array}$

Assume the population standard deviation is $\sigma = 36$ and that the population is approximately normal. Construct a 90% confidence interval for the operational time before failure.
A) (318.9, 358.4)
B) (331.3, 346.1)
C) (279.4, 397.9)
D) (332.1, 345.3)

Question

A random sample of electronic components had the following operational times before failure, in hours.

$\begin{array} { l l l l l } 
\hline 322 & 350 & 346 & 347 & 335 \
\hline 323 & 341 & 355 & 329 & \
\hline
\end{array}$

Assume the population standard deviation is $\sigma = 36$ and that the population is approximately normal. Construct a 90% confidence interval for the operational time before failure.
A) (318.9, 358.4)
B) (331.3, 346.1)
C) (279.4, 397.9)
D) (332.1, 345.3)

Quizplus · Accepted Answer

The confidence interval is calculated using the formula for a population mean with a known standard deviation: $\bar{x} \pm Z \frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $Z$ is the Z-value corresponding to the confidence level (for 90%, $Z = 1.645$), $\sigma$ is the population standard deviation, and $n$ is the sample size. Calculating the sample mean of the given data yields $\bar{x} = 339.7$, and with $n = 9$, the confidence interval calculation results in (318.9, 358.4).

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A Random Sample of Electronic Components Had the Following Operational $\begin{array} { l l l l l } \hline 322 & 350 & 346 & 347 & 335 \\\hline 323 & 341 & 355 & 329 & \\\hline\end{array}$