Choose the one alternative that best completes the statement or answers the question.
-A random sample of 150 towns in a western state had an average annual precipitation of $2.86$ inches and a population standard deviation of $0.78$ inches. Compute the $98 \%$ confidence interval for $\mu$.
A) $( 2.71,3.01 )$
B) $( 2.51,3.53 )$
C) $( 2.43,3.79 )$
D) $( 2.31,3.88 )$

Question

Quizplus · Accepted Answer

To compute the 98% confidence interval for the population mean $\mu$, we use the formula for the confidence interval when the population standard deviation is known, which is $\bar{x} \pm Z \frac{\sigma}{\sqrt{n}}$, 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 98% confidence level, the Z-score is approximately 2.33. Plugging in the given values: $2.86 \pm 2.33 \times \frac{0.78}{\sqrt{150}}$, we get the interval $(2.71, 3.01)$.

Choose the One Alternative That Best Completes the Statement or Answers