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
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?
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