You are the team chief of a task force with expertise for solving problems of a

Question

You are the team chief of a task force with expertise for solving problems of a logistics nature. Your team inspects a supply activity (such as a warehouse or depot). Your job is to identify major problem areas. The distribution for the number of major discrepancies your team sees (represented by X) is given in the table below. Complete the table and find the population mean, variance, and standard deviation. You are the quality control manager of a series of assembly line operations that produce small car parts. From historical records, you realize that the chance of producing a defective part is 7%. It is believed that the appearance of one bad part on the line has no impact on the status of the parts following it on the line A. Of the next ten parts coming off the assembly line, what's the probability that none will be bad? B. What is the probability that at most two will be defective? What's the probability that at least one will be bad? What is expected number of bad ones that you would see if you took many samples of 10 parts from the line? If you increase the sample size from 10 to 20 items, what's the probability that at least one will be bad? One of the samples containing 10 items from the Problem #2 above was put in a bin. You are told that four of these ten items were determined to be defective. However, none of the parts was labeled as good or bad. You select two of them without replacement. What's the probability that both are good? What is the probability that one of the two you select is defective? What's the probability that neither of the two is a good part? The average number of shipments that arrive at a landing area within a depot is three per hour during a regular business day. The process can be modeled with the Poisson distribution. These shipments arrive randomly, and are not related to each other in any way. a. What is the probability that more than two will arrive in a one-hour period? b. What is the chance that an hour goes by, and no shipments arrive? c. What is the probability that 2 hours go by and no more than two shipments arrive at the platform?

Explanation / Answer

2)

This is a binomial distribution, with n = 10, p = 0.07

P(X = x) = P(x of the 10 parts are bad)
............. = C(10,x) (0.07)^x (0.93)^(10-x)

——————————————————————————————

P(X=0) = 0.93^10 = 0.483982307 = 48.3982%

P(X2) = P(X=0) + P(X=1) + P(X=2)
= 0.483982307+ 10 (0.07) (0.93)^9 + 45 (0.05)^2 (0.95)^8

=0.483982307+0.3642877+0.123387789
= 0.971657796
97.165%

P(X1) = 1 P(X<1)
= 1 P(X=0)
= 1 0.483982307
=0.5160177
= 51.60177%

E(X) = n * p = 10 * 0.07= 0.7

If sample size is increased to 20 items, then

P(X1) = 1 P(X<1)
= 1 P(X=0

= 1 0.93^20

= 0.765761126
= 76.58%

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

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