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 values Would separate the 16% of orders that take the least 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 lowest 16% of orders, we use the Z-score formula for the normal distribution. The Z-score corresponding to 16% in a standard normal distribution table is approximately -1. (It's actually closer to -0.994, but -1 is a commonly used approximation for simplicity.) 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)(1.24) = 6 - 1.24 = 4.76 minutes.

The Time It Takes to Process Phone Orders in a Small