In a small town there are 10,000 homes. When it comes to television viewing, the residents havethree choices: they can subscribe to cable, they can pay for satellite service, or they watch no TV.(The town is sufficiently remote so that an antenna does not work.) In any given year, 80% of thecable customers stick with cable, 10% switch to satellite, and 10% quit watching TV. Over thesame time period, 90% of satellite viewers continue with satellite service, 5% switch to cable,and 5% quit watching TV. And of those people who start the year not watching TV, 85%continue not watching, 5% subscribe to cable, and 10% get satellite service (see Figure 1).Suppose that the current distribution is 5000 homes with cable, 3000 homes with satellite, and2000 homes with no TV. Find the distribution one year, two years, three years, and four yearsfrom now.85%10%5%CableƆ80%No TV10%5%5%10%Satellite90%Figure 1

The current distribution with cable = 5000 homesThe distribution with satellite = 3000 homesThe…

Answered: In a small town there are 10,000 homes.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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In a small town there are 10,000 homes. When it comes to television viewing, the residents have three choices: they can subscribe to cable, they can pay for satellite service, or they watch no TV. (The town is sufficiently remote so that an antenna does not work.) In a given year, 80% of the cable customers stick with cable, 10% switch to satellite, and 10% quit watching TV. Over the same time period, 90% of satellite viewers continue with satellite service, 5% switch to cable, and 5% quit watching TV. And of those people who start the year not watching TV, 85% continue not watching, 5% subscribe to cable, and 10% get satellite service (see Figure below). Suppose that the current distribution is 8000 homes with cable, 1300 homes with satellite, and 700 homes with no TV. Find the distribution one year, two years, three years, and four years from now. (A graphing calculator is recommended. Round your answers to the nearest integer.) A = .80 .05 .05 .10 .90 .10 .10 .05 .85 cable satellite…
On a particular night, a baseball stadium sells 60% of its seats, and of those, 15% do not end up showing up to the game. Assuming everyone present is sitting in a seat, what percentage of seats in the stadium are empty?
Sarah believes that completely cutting caffeine out of a person's diet will allow him or her more restful sleep at night. In fact, she believes that, on average, adults will have more than two additional nights of restful sleep in a four-week period after removing caffeine from their diets. She randomly selects 8 adults to help her test this theory. Each person is asked to consume two caffeinated beverages per day for 28 days, and then cut back to no caffeinated beverages for the following 28 days. During each period, the participants record the numbers of nights of restful sleep that they had. The following table gives the results of the study. Test Sarah's claim at the 0.05 level of significance assuming that the population distribution of the paired differences is approximately normal. Let the period before removing caffeine be Population 1 and let the period after removing caffeine be Population 2. Numbers of Nights of Restful Sleep in a Four-Week Period With Caffeine 24 22 24 20…
In a study carried out among low-income families in the young towns of Detroit, it was found that 30% spent less than $8 weekly on purchasing charcoal and consumed products from soup kitchens. 35% spent $8 to $15 weekly on the purchase of charcoal. 5% spent more than $15 weekly on the purchase of charcoal and consumed products from the soup kitchen. 15% spent more than $15 each week buying coal. Finally, 55% did not consume the products of the soup kitchens.If you randomly choose a low-income familyto. What is the probability that you spend less than $8 weekly on purchasing coal?b. What is the probability that you do not consume the products of the soup kitchens and spend 8 to 15 dollars buying charcoal?C. If the family spends more than $15 weekly on purchasing charcoal, what is the probability that they will not consume the products from the soup kitchens?d. If the family does not consume products from soup kitchens, what is the probability that it will spend less than 8 soles per…
Part 1: The state of Maryland's arrest rate for marijuana possession in 2010 was the fourth highest in the nation. Public records for that year show that police arrested one out of every 250 Maryland residents for possession of marijuana. In addition, while Black people only comprised 30% of the State's population in 2010, 58% of those arrested for marijuana possession were Black. Use the following labels for events describing Maryland residents in the year 2010. M-AMP: Maryland resident was arrested for marijuana possession M-B: Maryland resident was a Black person a) What is the probability that a Maryland resident was arrested for marijuana possession in 2010? b) Use probability notation to express the cited percent values. 30% = P( 58% = P( c) Which of the values cited should be compared to determine whether race and arrests for marijuana possession in the state of Maryland in 2010 are independent?
In a US presidential election, the incumbent president wins with 51.5% of the vote to 48.2% for the primary challenger (and .3% to others). In a nationwide telephone poll of 1000 people conducted exactly one week before the election by a university polling group, 49% of people polled supported the incumbent president, 50% supported the challenger, and 1% supported other candidates. a. For the polling study, what was the population of interest? b. What was the sample? c. Why did the sample results differ from the population? d. What are two constants that might have limited the generalizability of the polling results?
A car wash has three different types of washes: basic, classic, and ultimate. Based on records, 45% of customers get the basic wash, 35% get the classic wash, and 20% get the ultimate wash. Some customers also vacuum out their cars after the wash. The car wash records show that 10% of customers who get the basic wash, 25% of customers who get the classic wash, and 60% of customers who get the ultimate wash also vacuum their cars. The probabilities are displayed in the tree diagram.What is the probability that a randomly selected customer purchases the basic or classic car wash if they vacuum their car?A) 0.13B) 0.48C) 0.52D) 0.80
An ad agency is developing a campaign to promote a business opening in new mall development. To develop an appropriate mailing list, they decide to purchase lists of credit card holders from MasterCard and American Express. Combining the lists, they find the following: 40 percent of the people on the list have only a MasterCard and 10 percent have only an American Express card. Another 20 percent hold both MasterCard and American Express. Finally, 30 percent of those on the list have neither card. The contingency table is as the following: MasterCard No MasterCard .10 American Express 20 No American Express.40 What is the probability that a person on the list does not have a Mastercard? Select one: O a. .90 O b. 40 O C. .18 d. .33 e. .70
You're a quality engineer at Norman's fouth largest cracker factory. where there are two production lines (A, which produces 20% of cracker boxes, and B which produces the rest). If a line produces more than one defective box in an eight -hour day, a maintenance check on the line is performed. Line A produces an average of 0.061 box defects PER Hour. Given that you're only looking at a line A, what is the probability that you will need a request a maitenance check.
Three businesswomen are trying to convene in Cincinnati for a business meeting. The first women (Woman 1) is arriving on a flight from Atlanta, the second (Woman 2) is arriving on a flight from Dallas, and the third (Woman 3) is arriving on a flight from Chicago. Historical data suggests that the Atlanta flight is “on time” 90% of the time, the Dallas flight is “on time” 95% of the time, and the Chicago flight is “on time” 80% of the time. Furthermore, historical data suggests that the three flights are independent with respect to on time behavior. Define the sample space for this random experiment. Compute the probability for each of the outcomes in the sample space. Let W denote the number of business women that arrive on time. Construct the probability mass function of W Construct the cumulative distribution function of W Find the expected value of W Compute the standard deviation of W

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