A small flower shop takes orders by phone and then one of the staff florists is assigned to prepare the arrangement.The time it takes to process phone orders is normally distributed
With a mean of 6 minutes and a standard deviation of 2.5 minutes.The time it takes for an
Arrangement to be completed is normally distributed with a mean of 35 minutes and a
Standard deviation of 8.6 minutes.What is the probability that it will take more than 50
Minutes to process a phone order and complete the floral arrangement at this flower shop?
A)0.8413
B)0.3413
C)0.2167
D)0.1587
E)0.6843

Question

Quizplus · Accepted Answer

To find the probability that the total time (time to process a phone order plus time to complete the arrangement) exceeds 50 minutes, we first determine the mean and standard deviation of the total time. The mean of the total time is the sum of the means (6 minutes for phone orders + 35 minutes for arrangement completion = 41 minutes). The standard deviation of the total time is the square root of the sum of the squares of the individual standard deviations (√(2.5^2 + 8.6^2) ≈ 9 minutes). Using the normal distribution, we calculate the Z-score for 50 minutes: Z = (50 - 41) / 9 ≈ 1. The probability of a Z-score greater than 1 is approximately 0.1587, indicating the probability of the total time exceeding 50 minutes.

A Small Flower Shop Takes Orders by Phone and Then