Complete the below:
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 0.14 24 0.32
48 0.27 48 0.45
60 0.33 72 0.23
72 0.26
Total Time is the sum of Manufacturing Time and Shipping Time.
a. Show the Cumulative Distribution and Random Ranges for Manufacturing Time and Shipping Time.
b. Simulate Total Time in Bill's Manifolds, Inc for 10 manifold orders.
c. Compute the mean and standard deviation of Total Time in the shop (Assume Sample).
d. 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?