3. Many manufacturers have quality control programs that include inspection ofincoming materials for defects. Suppose a computer manufacturer receives circuitboards in batches of five. Two boards are selected from each batch for inspection. Wecan represent possible outcomes of the selection process by pairs. For example, thepair (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. Twoboards are to be chosen at random. Define X to be the number of defectiveboards observed among those inspected. Find the probability distribution of X.c. Let F(x) denote the cdf of X. First determine F(0) = P(X <0), F(1), and F(2);then obtain F(x) for all other x.

Answered: 3. Many manufacturers have quality…

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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5. An office manager is looking to purchase a new printer for his office. He has narrowed his choices down to four printers but cannot decide which of the four he prefers. He has decided to choose two of the four printers at random, and then to let the other members of the office decide which of the two they prefer. The speeds, in pages per minute, of the four printers are 25, 30, 27, and 32. Considering the speeds of the two printers chosen to be the sample, what are the mean and the standard deviation of the sample mean?
9. A group of 50 single men were asked which dating apps they had on their phones. The follo data were collected: 33 of the men had the Tinder app. 30 of the men had the Coffee Meets Bagel app. 26 of the men had the Hinge app. 16 of the men had both the Tinder and Coffee Meets Bagel apps. 14 of the men had both Tinder and Hinge apps. 18 men had both Hinge and Coffee Meets Bagel apps. 7 men had all three apps on their phones. a) Represent this information in a Venn diagram: b) Calculate the number of single men who have none of these apps on their phone. c) How many single men only had Tinder on their phone? d) How many students own at most two of the apps?
(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 firm employs 10 programmers, 8 systems analysts, 4 computer engineers, and 3 statisticians. A "team" is to be chosen to handle a new long-term project. The team will consist of 3 programmers, 2 systems analysts, 2 computer engi-neers and statistician (a)In how many ways can the team be chosen? (B)
In 2018, a consumer goods giant had more than 20 brands with more than $1 billion in annual sales. How does the company create so many successful consumer products? They effectively invests in research and development to understand what consumers want. One method used to determine consumer preferences is called conjoint analysis. Conjoint analysis allows a company to ascertain the utility that a respondent in the conjoint study places on a design of a given product. The higher the utility, the more valuable a respondent finds the design. Suppose we have conducted a conjoint study and have the following estimated utilities (higher is preferred) for each of three different designs for a new whitening toothpaste. Respondent Utilities Design A Design B Design C 1 24.6 34.4 28.8 2 31.4 31.4 33.9 3 31.8 20.2 27.8 4 15.4 26.4 25.1 5 20.7 18.3 18.2 6 41.0 34.0 44.8 7 27.1 22.5 27.3 8 20.2 21.8 27.9 9 31.6 29.4 31.3 10 24.4 29.0 29.3 At the 0.05 level of…
12. (18 pts) In a survey of 203 professional athletes, it was found that 98 of them owned a convertible, 86 of them owned a giant screen TV, and 98 owned a sporting goods store. 25 owned a convertible and a store, 36 owned a TV and a store, and 51 owned a convertible and a TV. 15 owned all three items. a. How many athletes did not own any of the three items? b. How many owned à convertible and a TV, but not a store? 36 c. How many athletes owned a convertible or a TV? d. How many athletes owned exactly one type of item in the survey? e. How many athletes owned at least one type of item in the survey? f. How many owned a TV or a store, but not a convertible?
7. A new drug study was conducted by a drug company. In the study, 10 people were chosen at random to take Vitamin X for 3 months and then have their cholesterol levels checked. In addition, 10 different people were randomly chosen to take Vitamin Y for 3 months and then have their cholesterol levels checked. All 20 people had cholesterol levels between 8 and 10 before taking one of the vitamins. The drug company wanted to see which of the 2 vitamins had the greatest impact on lowering people's cholesterol. The following data was collected: Vitamin X 7.27.5 5.2 6.5 7.7 10 6.47.6 7.77.8 Vitamin Y 4.8 4.44.5 5.1 6.5 8.03.1 4.6 5.2 6.1 (a) Draw a box-and-whisker plot for both sets of data on the same number line. (b) Use the double box-and-whisker plots to compare the 2 vitamins and provide a conclusion for the drug company. (e) State the skewness of both distributions and justify your answer.
6.2
1. For her botany class project, Jennifer wonders if there is a connection between the average weight of watermelons a vine produces and the root depth of the vine. Jennifer suspects that vines with deeper roots have a better water supply and produce larger melons. From a large watermelon field, 10 vines are chosen at random. At the end of 8 weeks, the watermelons are removed from each vine and the average weight of the watermelons from each vine is determined. Each plant is carefully dug up and its root depth (or length) is measure. Let x represent the root depth (to the nearest inch) and y be the mean weight of the watermelons on the vine (in pounds). Suppose that x = 17, s, = 6, y = 12, s, = 5.1, and r = = 0.93. a. Find the equation of the least squares regression line (round a and b to the nearest tenth). b. List 2 points that you know will be on the least-squares line you found in part a. c. What percent of variation is accounted for by a linear relationship? d. Using part a.,…
2. Mobile phone operator TELE2 has at least 4 tariffs: Brivais(B), Savejis(S), Smart(SM), Zelts(Z). In 2019Y the proportion of clients for each tariff is: B=5%; S=50%; SM-15%; Z=30%. Possible changes from one type of tariff to another for the following year are the following: to B to S to SM to Z from B 5% 2% 1% 1% 1% from S 3% 1% from SM 5% 5% from Z 5% 4% 3% Find initial distribution, Transition matrix (stochastic matrix), stationary distribution and plot a graph for transition of one step. bain ic the following
A researcher randomly selected 158 personal vehicles and noted the type of vehicle and its color. The two-way table displays the data. A 5-column table with 4 rows. Column 1 has entries sedan, S U V, convertible, total. Column 2 is labeled Red with entries 14, 9, 20, 43. Column 3 is labeled Blue/Green with entries 31, 19, 6, 56. Column 4 is labeled Black/Gray with entries 22, 34, 3, 59. Column 5 is labeled Total with entries 67, 62, 29, 158. The columns are titled Vehicle color and the rows are titled vehicle type. Suppose a vehicle is randomly selected. Let event C = convertible and R = red. What is the value of P(R|C)? StartFraction 29 Over 158 EndFraction StartFraction 43 Over 158 EndFraction StartFraction 20 Over 43 EndFraction StartFraction 20 Over 29 EndFraction

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