Choose the one alternative that best completes the statement or answers the question.
-In a random sample of 60 laptop computers, the mean repair cost was $\$ 150$ with a population standard deviation of $\$ 36$. Compute the $99 \%$ confidence interval for $\mu$.
A) $( \$ 138 , \$ 162 )$
B) $( \$ 18 , \$ 54 )$
C) $( \$ 238 , \$ 274 )$
D) $( \$ 537 , \$ 654 )$

Question

Quizplus · Accepted Answer

To compute the 99% confidence interval for the mean repair cost, we use 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-value corresponding to the desired confidence level (for 99%, $Z \approx 2.576$), $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $150 \pm 2.576 \frac{36}{\sqrt{60}}$, we get the interval $(\$138, \$162)$.

Choose the One Alternative That Best Completes the Statement or Answers