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, we use the Z-score formula for the 97.5th percentile (since 100% - 2.5% = 97.5%). Looking up the Z-score for 97.5% in a standard normal distribution table gives us approximately 1.96. Using the formula for a specific value in a normal distribution, X = μ + Zσ, where μ is the mean (6 minutes), σ is the standard deviation (1.24 minutes), and Z is the Z-score (1.96), we calculate X = 6 + (1.96)(1.24) ≈ 8.48 minutes.

The Time It Takes to Process Phone Orders in a Small