A manufacturer produces test tubes from two independent processes. Process 1 produces
10% defectives while Process 2 produces 15% defectives. Random samples of size 100
are obtained from each process on a daily basis. What is the probability that the sample
from Process 1 has fewer defectives than the of Process 2?
The number of defectives out of 100 from process 1 has Binomial distribution with . The normal approximation is
The number of defectives out of 100 from process 2 has Binomial distribution with . The normal approximation is
Since and are independent, .
The required probability is
A manufacturer produces test tubes from two independent processes. Process 1 produces 10% defectives while Process...
The following data gives the number of defectives in 5 independent samples from a production process. The samples are of varying size. Draw appropriate chart and comment on the process Sample number Sample size Number of defectives 1 2000 400 2 1000 150 3 1000 120 4 600 80 5 400 50
A manufacturer produces a component for use in the automotive industry. It is known that 1% of the items produced are defective. Suppose a random sample of 20 items is examined. (a) Find the probability that (i) no defectives are found in the sample, (ii) one or fewer defectives are found in the sample. (b) Find: (i) the mean (expected) number of defectives in the sample, (ii) the variance and standard deviation.
For a comparison of the rates of defectives produced by two assembly lines, independent random samples of 100 items were selected from each line. Line A yielded 18defectives in the sample, and line B yielded 12 defectives.a) Create a 90% confidence interval for the true difference in proportions of defectives for the two lines.b) Interpret the confidence interval you constructed in part (a) in the context of the problem.c) Based on your answer in part (a), is there evidence to...
A manufacturer of computer memory chips produces chips in lots of 1000. If nothing has gone wrong in the manufacturing process, at most 7 chips each lot would be defective, but if something does go wrong, there could be far more defective chips. If something goes wrong with a given lot, they discard the entire lot. It would be prohibitively expensive to test every chip in every lot, so they want to make the decision of whether or not to...
2) A bicycle component manufacturer produces hubs for bike wheels. Two processes are possible for manufacturing, and the parameters of each process are as follows Process 1 Process 2 Production rate Daily production time Percent of parts rejected based on visual inspection 35 parts/hour 4 hours/day 20% 15 parts/hour 7 hours/day 9% Assume that the daily demand for hubs allows all defect-free hubs to be sold. Additionally, tested or rejected hubs cannot be sold Find the process that maximizes profit...
1. Suppose a manufacturer has plants at two different locations. From the long-time observations, it is known that approximately 5% and 8% defectives are produced at these two locations. Random samples of 300 items are selected from one week's production at each location. What is the likelihood that the sample proportions will differ by less than 1%.
Let ??1(??) and ??2(??) be two independent Poisson processes with rates ??1 = 1 and ??2 = 2, respectively. Find the probability that the second arrival in ??1(??) occurs before the third arrival in ??2(??). Hint: One way to solve this problem is to think of ??1(??) and ??2(??) as two processes obtained from splitting a Poisson process.
Zip, Inc. manufactures Zip drives on two different manufacturing processes. Because the management of this company is interested in determining if process 1 takes less manufacturing time, they selected independent random samples from each process. The results of the samples are shown below. Process 1 Process 2 Sample size, n 12 22 Sample mean (in minutes) 58 64 sample standard deviation, s 9 25 a. State the null and alternative hypotheses. b. Determine the degrees of freedom for the t...
Zip, Inc. manufactures Zip drives on two different manufacturing processes. Because the management of this company is interested in determining if process 1 takes less manufacturing time, they selected independent random samples from each process. The results of the samples are shown below. Process 1 Process 2 Sample size, n 12 22 Sample mean (in minutes) 58 64 sample standard deviation, s 9 25 a. State the null and alternative hypotheses. b. Determine the degrees of freedom for the...
Summary is obtained from two independent Normal samples a). Test whether one can assume equal variances. b) With a suitable test procedure, test for equality of means . Sample1 20 28 8 Sample2 40 Sample size Sample mean Sample standard deviation 10