A manufacturing process produces, on the average, 3% defective items. The compan

Question

A manufacturing process produces, on the average, 3% defective items. The company ships 10 items in each box. Let X denote the number of defective items found in a randomly chosen box (a) Find the mean and standard deviation of X. (b) The company guarantees that no more than one defective item will be found in a box. What is the probability that a randomly chosen box will fail to satisfy the guarantee? That is, what is the probability that a randomly chosen box will have 2 or more defective items.)

Explanation / Answer

(a) Mean and standard variation are for a range of values (Is some info missing)

(b) Probability that an item is defective 0.03

Probability that two items are defective = (0.3) * (0.3) = (0.3)2

Probability that atleast two are defective = (0.3) 2 +(0.3)3 + ........ (0.3) 10

By geometric series sum we have this as

(0.3) 2 ( 1- 0.3 9 )/(1-0.3)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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