4.14 points] If a production line has a 20% defective rate. What is the mean and...
20% of the items on a production line are defective. Randomly insptect items, and let X1 be the number of inspections till the first defective item is observed, and X5 be the number of inspections till the fifth defective item is observed. In both cases, X1 and X5 inlcude the defective item itself (e.g. if the items are {good, good, defective), X1 is 3). Calculate E (%). V (Xs)
Suppose 20% of the engines manufactured on a certain assembly line are defective. If engines are randomly selected one at a time and tested. a. Find the probability that first defective engine is found on the third trial. b. Find the mean and variance of the number of the trial on which the first defective engines is found.
Number 12 9. In a production process, one fifth of the items fabricated are defective. Ten items from the production line are randomly selected and inspected. Let X be the number of defective articles in this sample. If the distribution of X is Bin(n,p), what are the values of n and p? 10. of the random variable X is given. What is the mean of the distribution? 11. What is of the distribution? 12, X is a random normal normal...
Off the production line, there is a 2.2% chance that a candle is defective. If the company selected 40 candles off the line, what is the standard deviation of the number of defective candles in the group?
A production line has 4% of its products defective. If 25 pieces are sampled, with replacement, what is the probabilty of finding 2 that are defective?
Three machines first has an output of 20% with defective rate of 5%, second has an output of 30% with defective rate of 3%, and last has an output of 50% with defective rate of 1%. If you randomly selected a defective part what is the probability that it came from the third machine?
Approximately 20% of the lightbulbs produced by a company are defective (and the rest are non-defective). Suppose 3 lightbulbs are selected randomly. Let Y be the random variable showing number of defective lightbulbs. a)Complete the following probability distribution given in the following table. (You can use binomial distribution formula) y p(y) 0 0.512 1 2 3 0.008 Find the mean and variance of the above probability distribution
9. A production process produces components of which 2 percent are defective. a) What is the expected number of components produced before a defective one is made? b) What is the probability that the first defective component will occur within the first five components off the line? c) What is the probability that the first defective component will occur within the first 50 components?
A production station has a naturally occurring rate of unexpected breakdowns. The mean time between interruptions is 6 hours. The average repair time is 20 minutes, and the CV for repair time is 1.75. The mean natural processing time is 10 minutes with standard deviation 1 minute. a. What is the effective processing time and the CV of effective process time? b. If the arrival rate to the station is 5 jobs per hour, what is the station’s utilization? c....
There are 5% defective parts manufactured by your production line, and you would like to find these before they are shipped. A quick and inexpensive inspection method has been devised that identifies 8% of parts as defective. Of parts identified as defective, 50% are truly defective. a. Complete a probability tree for this situation. b. Find the probability that a defective part will be identified (ie, the conditional probability of being identified given that the part was defective). c. Find...