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 95% confidence interval for the population mean of waiting times is ________.A. 14.02 to 15.98B. 7.16 to 22.84C. 14.06 to 15.94D. 8.42 to 21.58E. 19.80 to 23.65

Answer 1

Answer: A. 14.02 to 15.98

Explanation:

Let
`\mu` denotes the mean waiting time for population.

Given : Sample size : n= 64

Sample mean :
`\overline{x}=15` (minutes)

Population standard deviation =
`\sigma= 4`

Confidence level : 95%

By z-table , the critical values for 95% confidence = z*=1.96

Confidence interval for population mean :
`\overline{x}\pm z^* (\sigma)/(√(n))`

The 95% confidence interval for the population mean of waiting times will be :

`15\pm (1.96)(4)/(√(64))`

`15\pm (1.96)(4)/(8)`

`15\pm (1.96)(0.5)`

`15\pm 0.98`

`(15-0.98,\ 15+0.98)=(14.02,\ 15.98)`

Hence, the 5% confidence interval for the population mean of waiting times is 14.02 to 15.98.

Thus , the correct answer is Option A.