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 standard deviation for the total time to process a phone order and complete the floral arrangement at this flower shop (assuming times are Independent)?
A)8.96 minutes
B)41 minutes
C)80.28 minutes2
D)4.87 minutes
E)12.43 minutes

Question

Quizplus · Accepted Answer

The total time to process a phone order and complete the floral arrangement is the sum of the two independent normally distributed random variables. The variance of the sum of two independent random variables is the sum of the variances of the individual random variables. Therefore, the variance of the total time is (2.5)^2 + (8.6)^2 = 80.28. The standard deviation is the square root of the variance, so the standard deviation of the total time is sqrt(80.28) = 8.96 minutes.

A Small Flower Shop Takes Orders by Phone and Then