4. Suppose that the following data were obtained from the records of a certain two yearcollege: Of those who were freshman (F) during a particular year, 80% become sopho-mores (S) during the next year and 20% dropped out. Of those who were sophomoresduring a particular year 90% graduated (G) by the next year and 10% dropped out.(a) Create a transition diagram that describes this scenario.(b) Create a transition matrix that describes this scenario. Is this scenario ergodic orabsorbing? Explain.(c) Suppose that this year, there are an equal percentage of freshmen and sophomores.Use matrix multiplication to determine what percentage will have graduated in 5years? What percentage will have dropped out?(d) Rewrite the matrix in standard form.(e) Find N, R and B.(f) Determine the probability that a student who begins as a freshman will drop out.(g) Determine the probability that a student who has made it to sophomore year willdrop out.(h) Determine the probability that a student who begins as a freshman will graduate.(i) Determine the probability that a student who has made it to sophomore year willgraduate.

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Answered: 4. Suppose that the following data were…

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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The following is based on information from The Wolf in the Southwest: The Making of an Endangered Species, by David E. Brown (University of Arizona Press). Before 1918, the proportion of female wolves in the general population of all southwestern wolves was about 50%. However, after 1918, southwestern cattle ranchers began a widespread effort to destroy wolves. In a recent sample of 37 wolves, there were only 11 females. One theory is that male wolves tend to return sooner than females to their old territories, where their predecessors were exterminated. Do these data indicate that the population proportion of female wolves is now less than 50% in the region? Use α = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: P 0.5 O Ho: P = 0.5; H₁: p 5 and nq > 5. O The Student's t, since np > 5 and ng > 5. The standard normal, since np < 5 and nq < 5. O The Student's t, since np < 5 and nq < 5. What is the value of the sample test statistic? (Round…
Data from the Bureau of Labor Statistics indicates that in a certain month, 35.7% of the labor force had a high school diploma or fewer years of education, 29.4% had some college or an associate's degree, and 34.9% had a bachelor's degree or more education. Of those with a high school diploma or fewer years of education, 5.5% were unemployed. Of those with some college or an associate's degree, 4.4% were unemployed, and of those with a bachelor's degree or more education, 2.4% were unemployed. Find the probability that a randomly chosen labor force participant has some college or an associate's degree given that he or she is unemployed. 12 The probability is 0 (Type an integer or decimal rounded to three decimal places as needed.)
1. A machine can be in one of four states: 'running smoothly' (state 1), 'running but needs adjustment' (state 2), 'temporarily broken' (state 3), and 'destroyed' (state 4). Each morning the state of the machine is recorded. Suppose that the state of the machine tomorrow morning depends only on the state of the machine this morning subject to the following rules. • If the machine is running smoothly, there is 1% chance that by the next morning it will have exploded (this will destroy the machine), there is also a 9% chance that some part of the machine will break leading to it being temporarily broken. If neither of these things happen then the next morning there is an equal probability of it running smoothly or running but needing adjustment. • If the machine is temporarily broken in the morning then an engineer will attempt to repair the machine that day, there is an equal chance that they succeed and the machine is running smoothly by the next day or they fail and cause the machine…
The following table presents the orders of Samson Company for the last 36 months (3 years). Month Order Year 1 Order Year 2 Order Year 3 January 450 600 612 February 418 575 668 March 490 580 680 April 451 534 653 May 466 555 674 June 511 604 702 July 522 624 724 August 500 612 716 September 502 633 712 October 523 634 724 November 533 643 735 December 534 676 755 Use the data in the above table and regression analysis to forecast the orders for the next 12 months (4th year). Include your excel work sheet and your work in your write up. Show the regression equation, values of intercept, slope, correlation coefficient and coefficient determination and the forecast of orders for the next 12 months. Explain how you could make your forecast’s results more reliable by incorporating a qualitative research to your quantitative results.
Suppose a researcher is interested in examining the relationship between a person's gender and whether he or she likes the taste of Vegemite (a dark- brown food paste, made from yeast, that is popular in Australia). She collects a sample of n = 10 people and asks them whether they like the taste of Vegemite. The following table summarizes the results. Male Female Does Not Like the Taste of Vegemite 4 1 Likes the Taste of Vegemite 2 3 The researcher wants to calculate the correlation between a person's gender and whether he or she likes the taste of Vegemite. To do so, the researcher first creates a table of the data by converting each variable to a numerical value. She assigns 0 to "male" and 1 to "female." She then assigns 0 to "does not like the taste of Vegemite" and 1 to "likes the taste of Vegemite."
stüdentS (3) The population is classified by their economic status: poor, middle-class and rich. Every year, people moving up and down the economic ladder according to From: To: рoor middle-class rich 0.9 0.05 0.05 рor middle-class 0.1 0.8 0.1 rich 0.02 0.02 0.96 In year 2011, a 100-family town is made up of 30 poor, 40 middle-class and 30 rich families, a. what will be the makeup of this town in year 2012? b. what will be the makeup of this town in year 2015? c. what was the makeup of this town in year 2010?
1. A machine can be in one of four states: 'running smoothly' (state 1), 'running but needs adjustment' (state 2), 'temporarily broken' (state 3), and 'destroyed' (state 4). Each morning the state of the machine is recorded. Suppose that the state of the machine tomorrow morning depends only on the state of the machine this morning subject to the following rules. • If the machine is running smoothly, there is 1% chance that by the next morning it will have exploded (this will destroy the machine), there is also a 9% chance that some part of the machine will break leading to it being temporarily broken. If neither of these things happen then the next morning there is an equal probability of it running smoothly or running but needing adjustment. • If the machine is temporarily broken in the morning then an engineer will attempt to repair the machine that day, there is an equal chance that they succeed and the machine is running smoothly by the next day or they fail and cause the machine…
3. Travelers who have no intention of showing up often fail to cancel their hotel reservations in a timely manner. These travelers are known, in the parlance of the hospitality trade, as "no-shows". To protect against no-shows and late cancellations, hotels invariably overbook rooms. A recent study examined the problems of over-booking rooms in the hotel industry. The following data, extracted from the study represent the daily numbers of late cancellations and no-shows for a random sample of 10 days at a hotel: 18, 16, 16, 16, 14, 18, 16, 18, 14, 19. c) Count the number of measurements that actually fall within the interval(-28, +2s) and express the interval count as a percentage of total number of measurements. at least 75% 100% 68% 95%
Is the national crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 years†. Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of 37 arrests last month, 22 were of males aged 15 to 34 years. Use a 10% level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%.
The following table gives the annual revenue for two different companies (in billions of dollars) for a 10-year period. What is the five-number summary for Company A? Year 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 D Company A 97 97 60 105 87 100 70 101 109 95 96 84 Company B 45 65 66 70 73 82 93 83 ..... What is the five-number summary for company A? Q, =O Q2 =0 Q3 =D Max = Min = %3D (Type integers or decimals.)
The authors of a paper compared two different methods for measuring body fat percentage. One method uses ultrasound, and the other method uses X-ray technology. Body fat percentages using each of these methods for 16 athletes (a subset of the data given in a graph that appeared in the paper) are given in the accompanying table. You can assume that the 16 athletes who participated in this study are representative of the population of athletes. Athlete X-ray Ultrasound 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 5.00 8.00 9.25 12.00 17.25 29.50 5.50 6.00 8.00 13.50 9.25 11.00 12.00 14.00 17.00 18.00 4.25 4.75 9.00 11.75 17.00 27.50 6.50 6.75 8.75 14.50 9.50 12.00 12.25 15.50 18.00 18.25 Use these data to estimate the difference in mean body fat percentage measurement for the two methods. Use a confidence level of 95%. (Use μ = MX-ray-Multrasound. Round your answers to three decimal places.) × % Interpret the interval in context. O There is a 95% chance that the true mean body fat percentage…
Is the national crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 years†. Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of 36 arrests last month, 22 were of males aged 15 to 34 years. Use a 5% level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%. (a) What is the level of significance?State the null and alternate hypotheses. H0: p < 0 .7; H1: p = 0.7H0: p = 0 .7; H1: p < 0.7 H0: p = 0.7; H1: p > 0.7H0: p ≠ 0.7; H1: p = 0.7H0: p = 0.7; H1: p ≠ 0.7 (b) What sampling distribution will you use? The standard normal, since np < 5 and nq < 5.The Student's t, since np > 5…

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