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 normal distribution. The Z-score corresponding to the top 2.5% is approximately 1.96 (or specifically, 1.96 for the bottom 97.5%). We then apply the formula: X = μ + Zσ, where μ is the mean, Z is the Z-score, and σ is the standard deviation. Plugging in the values: X = 6 + (1.96)(1.24) ≈ 8.48 minutes.

The Time It Takes to Process Phone Orders in a Small