The time it takes to process phone orders in a small florist/gift shop is normally distributed with a mean of 6 minutes and a standard deviation of 1.24 minutes. What
Cutoff value would separate the 2.5% of orders that take the most time to process?
A) 3.52 minutes
B) 4.76 minutes
C) 8.48 minutes
D) 10.01 minutes
E) 11.98 minutes

Question

Quizplus · Accepted Answer

To find the cutoff value that separates the top 2.5% of orders (meaning we are looking for the 97.5th percentile in a normal distribution), we use the Z-score formula associated with the 97.5th percentile, which is approximately 1.96. The formula to convert a Z-score to an actual value is X = μ + Zσ, where μ is the mean, σ is the standard deviation, and Z is the Z-score. Plugging in the values: X = 6 + 1.96(1.24) = 6 + 2.4304 = 8.43, which rounds to approximately 8.48 minutes.

The Time It Takes to Process Phone Orders in a Small