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)

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).