Suppose that a customer service center claims that the telephone calls it receives last 112 seconds on average, with a standard deviation of 9 seconds. If you took a sample of 324 telephone calls, which of the following mean times would be within the 95% confidence interval?
A. 113.5 seconds
B. 114.5 seconds
C. 112.5 seconds
D. 115.5 seconds

Question

Suppose that a customer service center claims that the telephone calls it receives last 112 seconds on average, with a standard deviation of 9 seconds. If you took a sample of 324 telephone calls, which of the following mean times would be within the 95% confidence interval?
  		A. 	113.5 seconds
  		B. 	114.5 seconds
  		C. 	112.5 seconds
  		D. 	115.5 seconds

anonymous · Answer

The confidence interval has the form
$$\left(\bar{x}-Z_{\alpha/2}\frac{\sigma}{\sqrt n},~\bar{x}+Z_{\alpha/2}\frac{\sigma}{\sqrt n}\right)$$
where $\bar{x}$ is the sample mean (112 seconds), $Z_{\alpha/2}$ is the cutoff for the $(1-\alpha)100\%$ confidence level, $\sigma$ is the sample/population standard deviation (9 seconds), and $n$ is the sample size (324 callers).

Since the confidence level is 95%, you have $Z_{\alpha/2}=1.96$.

Construct the interval and check which of the listed values fall in its range.