# Compute the mean and standard deviation of Total Time in the shop

Simulation of manufacturing time for Bill’s Manifolds Inc

Work the following problem using an Excel Annotate and

Bill’s Manifolds, Inc produces made to order special
manifolds for motorcycles The total time from receipt of order until the
customer receives the product consists of two phases: 1) manufacturing time and
2) shipping time Manufacturing Time is a discrete random variable that ranges
from 36 to 72 hours with a distribution as shown below Shipping Time is also a
discrete random variable that ranges from 24 to 72 hours with a distribution as
shown below

Manufacturing Time Shipping
Time

X, Hours P(X) X, Hours P(X)

36 014 24 032

48 027 48 045

60 033 72 023

72 026

Total Time is the sum of Manufacturing Time and Shipping
Time

a(10) Show the Cumulative Distribution and Random Ranges
for Manufacturing Time and Shipping Time

b(10) Simulate Total Time in Bill’s Manifolds, Inc for 10
manifold orders

c(4) Compute the mean and standard deviation of Total Time
in the shop (Assume Sample)

d(3) If Total Time in the shop is a Normal Random Variable
with the mean and standard deviation that you calculated in d above, what is
the probability that an order will take less than 90 hours to process?

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