190k views
5 votes
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 ________.

User Marquita
by
7.3k points

1 Answer

4 votes

Answer: (14.18, 15.08)

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)(\sigma)/(√(n))\\\\=15\pm(1.645)(4)/(√(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).

User Felixqk
by
7.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.