a. What is the probability that the pack task takes more than 30 seconds? b. What is the probability that the entire process takes less than 120 seconds (two minutes), assuming that there is no time between tasks? Hint: the entire process requires completion of each task in the sequence shown. c. The industrial engineer times the entire process for a random sample of 15 orders (recall that there is no time between tasks). What is the probability that the entire process takes less than 120 seconds (two minutes) for at least 10 of the 15 orders in this sample? Hint: the entire process requires completion of each task in the sequence shown.

An industrial engineer is evaluating workflow in an online retail fulfillment

center. Online fulfillment involves three tasks which must be performed in the following

sequence: [1] pick the merchandise from inventory, [2] pack the merchandise in boxes, [3] ship

the packed boxes. The amount of time it takes to complete each task is normally distributed

with parameters given in the table below. Assume that the time it takes to complete each task

is independent of the other tasks).

Task Mean () Standard Deviation ()

Pick 61 seconds 23 seconds

Pack 27 seconds 12 seconds

Ship1 20 seconds 5 seconds

a. What is the probability that the pack task takes more than 30 seconds?

b. What is the probability that the entire process takes less than 120 seconds (two

minutes), assuming that there is no time between tasks? Hint: the entire process

requires completion of each task in the sequence shown.

c. The industrial engineer times the entire process for a random sample of 15 orders

(recall that there is no time between tasks). What is the probability that the entire

process takes less than 120 seconds (two minutes) for at least 10 of the 15 orders in

this sample? Hint: the entire process requires completion of each task in the

sequence shown.

d. For the same sample of 15 orders, what is the probability that the sample mean for

the entire process is less than 120 seconds (two minutes)? Hint: the entire process

requires completion of each task one after the other in the sequence shown.

e. By automating the ship task, the mean and standard deviation of this task’s time

would be cut in half, so the mean () = 10 seconds. If workers are paid $27/hour, or

$.0075/second, how much would the online retailer expect to save on labor for its

750,000 annual orders by automating?