The company you are working for just received an order for 10 castings, made from precious...

The company you are working for just received an order for 10 castings, made from precious
metals. The way the facility works is as follows: you first schedule n castings for production
and order the first materials necessary. Then, each of the n scheduled castings can turn out to
be of high quality with a probability of 0.90. All castings are produced independently. You can
only sell castings of high quality to the customer. Answer the following questions.
(a) Assume your company plans to produce n = 15 castings. What is the probability they get
at least 10 castings of high quality to sell to the customer?
(b) Now, assume your company plans to produce n = 10 castings. What is the probability they
get at least 10 castings (that is, exactly 10 castings out of the scheduled 10) of high quality to
sell to the customer?
(c) Based on your answers in (b) and (c), would you recommend they plan for 10 or 15 castings?
Summarize your reasoning in one sentence.
(d) Perform the same calculations for scheduling n = 11, 12, 13, 14. How many castings would
you opt to schedule? Show your results for each case of n and summarize your reasoning in a
sentence.

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Expert Solution

orchestra answered 1 year ago

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