James Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB.His staff randomly selected personnel files for 100 tellers in the southeast region and determined that their mean training time was 25 hours.Assume that the population standard deviation is 5 hours.The 88% confidence interval for the population mean of training times is ________.
A)17.25 to 32.75
B)24.22 to 25.78
C)24.42 to 25.59
D)19.15 to 30.85
E)21.00 t0 32.00

Question

Quizplus · Accepted Answer

The correct confidence interval is calculated using the formula for a confidence interval for the mean with a known population standard deviation, which is $\bar{x} \pm Z \frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $Z$ is the Z-score corresponding to the confidence level, $\sigma$ is the population standard deviation, and $n$ is the sample size. For an 88% confidence level, the Z-score is approximately 1.55. Plugging in the values ($\bar{x} = 25$, $\sigma = 5$, $n = 100$), we get the interval $25 \pm 1.55 \times \frac{5}{\sqrt{100}} = 25 \pm 0.775$, which simplifies to $24.225$ to $25.775$, rounded to $24.22$ to $25.78$, making option B the correct choice.