Question

Brian Vanecek, VP of Operations at Portland Trust Bank, is evaluating the service level provided to walk-in customers. Accordingly, his staff recorded the waiting times for 64 randomly selected walk-in customers and determined that their mean waiting time was 15 minutes. Assume that the population standard deviation is 4 minutes. The 90% confidence interval for the population mean of waiting times is ________.

Answer 1

Answer: (14.18, 15.08)

Step-by-step explanation:

Given : Sample size : n= 64

Sample mean : $\overline{x}=15$

Standard deviation : $\sigma=4$

Significance level : $\alpha: 1-0.90=0.1$

Critical value : $z_{\alpha/2}=1.645$

The confidence interval for population mean is given by :-

$\overline{x}\pm\ z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=15\pm(1.645)\dfrac{4}{\sqrt{64}}\\\\\approx15\pm0.82\\\\=(14.18,\ 15.08)$

Hence, the 90% confidence interval for the population mean of waiting times is (14.18, 15.08).