A manufacturer makes spools of fabric material to make suits for a company. The

Question

A manufacturer makes spools of fabric material to make suits for a company. The company has an agreement to buy 100 spools of material from the manufacturer yearly. Each spool consists of 10,000 square meters and costs $100,000. Rips appear in the material at a rate of 0.002 per 100 square meters of material. A worker randomly chooses one, 100-square meter of material from each of the 100 spools to be delivered to the company. If the sample from a spool of material has a rip, then the spool of material is returned to the manufacturer who must deliver a new spool for 75% of the original cost to the company (For example, the manufacturer gives a 25% rebate to the company on the returned spool). If the entire delivery is ripless, the manufacturer receives a 10% bonus on the entire delivery.

a. Find the probability that the worker will find at least one rip in a 100-square meter area of material.

b. Find the probability that the manufacturer will get a bonus.

c. If the worker finds more than two spools with rips, the delivery is canceled and company uses another source. The manufacturer then gets no money from company. Find the amount of money that the manufacturer can expect to obtain from the company in any given year of the agreement.

Explanation / Answer

n = number of spools = 100

p = Probability of finding a rip = 0.002

q = 1-0.002 = 0.998

a) P(at least one rip) = 1 - P(no rip)

= 1 - 0.998100

= 0.1814

b) P(getting bonus) = 0.998100 = 0.8186

c) P(1) = 100x0.002x0.99899 = 0.1640

P(2) = 100C2 x 0.0022 x 0.99898 = 0.0163

P(more than 2) = 1 - (0.8186 + 0.1640 + 0.0163) =

The amount of money that the manufacturer can expect to obtain from the company in any given year of the agreement = 0.8186x11,000,000 + (0.1640+0.0163)10,000,000 + 0

= $10,807,600

X = No of spools with rips 0 1 2 more than 2 P(X) 0.8186 0.1640 0.0163 0.0011 Amount paid to manufacturer 100x100,000 x 1.1 = $11,000,000 $10,000,000 $10,000,000 $0

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.