A company uses three machines for production. For each machine the numberof flaws in a produced item is poisson distributed. Machine A produces 55% ofeverything and has an average of 1/1000 flaws per item. Machine Bproduces 30% of everything and has an average of 3/1000 flaws. Machine Cproduces 15% of everything and has an average of 3/500 flaws. At the end allproduced items get mixed up and we randomly select one.(a) What is the expected number of flaws on that item?(b) What is the probability that the selected item has at least one flaw? (Roundto 5 decimal places)

A discrete random variable X is said to follow Poisson distribution with parameter λ, if its…

Answered: A company uses three machines for…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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#3) A systems specialist has studied the workflow of clerks all doing the same inventory work. Based on this study, she designed a new workflow layout for the inventory system. To compare the average production for the old and new methods, a random sample of 6 clerks was used. The average production rate (number of inventory items processed) for each clerk was measures both before and after the new system was introduced. The results are shown below. Test the claim that the new system speeds up the work rate (use a = 0.05) Clerk B: Old method A: New Method 4 85 3 97 2 110 100 117 101 118 112 115 83 125 109
rch A computer manufacturer is interested in comparing assembly times for two keyboard assembly processes. Assembly times can vary considerably from worker to worker, and the company decides to eliminate this effect by selecting 12 workers at random and timing each worker on each assembly process. Half of the workers are chosen at random to use Process 1 first, and the rest use Process 2 first. For each worker and each process, the assembly time (in minutes) is recorded, as shown in the table below. Worker Process 1 Process 2 Difference (Process 1 - Process 2) Send data to calculator 1 81 67 Explanation Type of test statistic: O 14 Check 2 80 78 2 3 84 65 19 89 72 17 5 81 78 (a) State the null hypothesis Ho and the alternative hypothesis H₁. Ho H₁ :0 (b) Determine the type of test statistic to use. 3 6 35 53 7 50 30 -18 20 8 32 34 LG -2 9 45 48 (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the two critical values at the 0.05…
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A mathematics researcher has pointed out a problem with massive, untargeted wiretaps. To illustrate the problem, he supposes that one out of every million citizens of a certain country has terrorist ties. Furthermore, he supposes that the terrorist profile is 98.4% accurate, so that if a person has terrorist ties, the profile will pick them up 98.4% the time, and if the person does not have terrorist ties, the profile will accidentally pick them up only 1.6% of the time. Given that the profile has picked up a person, what is t probability that the person actually has terrorist ties? The probability is (Type an integer or a decimal rounded to six decimal places as needed.)
There are X-Mart and Y-Mart convenience stores. It is assumed that each customer purchases once a week at one of the two supermarkets (but not both). In a study, a sample of 100 buyers was taken for 10 weeks. From this research it is known that if buyers go to X-mart store one week, 85 people will still buy at X-mart store the following week and if buyers go to Y-mart store one week, 70 people will still buy at Y-mart store. mart the following week. 1. Make a table and matrix of transition probabilities. 2. If John purchases at X-mart in the first week, what is the probability that Bob purchases at X-store in the third and fourth weeks?
(Devore: Section 3.2 #15) Many manufacturers have quality control programs that include inspec- tion of incoming materials for defects. Suppose a computer manufacturer receives circuit boards in batches of five. Two boards are selected from each batch of inspection. We can represent possible outcomes of the selection process by pairs. For example, the pair (1,2) represents the selection of boards 1 and 2 for inspection. (a) List the ten different possible outcomes. (b) Suppose that boards 1 and 2 are the only defective boards in a batch. Two boards are to be chosen at random. Define X to be the number of defective boards observed among those inspected. Find the probability distribution (pmf) of X. (c) Let F denote the cdf of X. Determine F(0), F(1) and F(2); then obtain F(x) for all other x.
A small ice cream parlor has had great success over the past several years and is interested in expanding into handmade chocolate candies. A poll of 56 randomly selected customers was asked if they would purchase these chocolate candies. Forty of the customers indicated that they would. Customers Stottetomers wto would nan eturer. d. The ice cream parlor needs at least 85% of its customers to purchase handmade chocolate candies to make this expansion profitable. Does it appear as if the expansion into handmade chocolate candies will be profitable? Explain.
A researcher wants to determine whether adolescents spend more time in a day around friends than adults do. He gathers a sample of n =10 adolescents (aged 12-17) and a sample of n =6 adults (aged 25-32). The researcher finds that the average time spent around friends for adolescents is M1= 3 hours with a SS1 of 44. He also finds that the average time spent around friends for adults is M2= 2 hours with a SS2 of 40. a. Do you use a one- or two-tailed test? What is the critical/cut-off t value with an alpha level of α = .01? b. What is the variance? c. What is the estimated standard error? d. What is the value of the t statistic? e. Do we reject or fail to reject the null hypothesis (α = .01)? Why? f. Calculate and report the variance explained ( r2)
The director of cooperative education at a state college wants to examine the effect of cooperative education job experience on marketability in the work place. She takes a random sample of 4 students. For these 4, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation. These data are presented in the table below. Student CoopJobs JobOffer 1 1 4 2 2 6 3 1 3 4 0 1 Graphical method: Show the slope of the line y- intercept Equation of the regression line SSE If coop jobs is 3 for the fifth student, what is the value of the job offer?
A researcher wishes to try three different techniques to lower the blood pressure of students diagnosed with high blood pressure in the school sickbay. The subjects are randomly assigned to three groups; the first group takes medication from the school nurse, the second group takes exercises led by the school sports master, and the third group follows a special diet from the school pantry. After four weeks, the reduction in each person’s blood pressure is recorded in the table below. TECHNIQUES Medication Exercise Diet 10 6 7 12 8 9 9 3 12 15 10 8 14 2. 5TOTAL 60 29. 41At α = 0.05, analyse this case study in a one way ANOVA
1

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