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

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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…
A large industrial firm uses 3 local motels to provide overnight accommodations for its clients. From past experience it is known that 20% of the clients are assigned rooms at the Ramada Inn, 50% at the Sheraton, and 30% at the Lakeview Motor Lodge. If the plumbing is faulty in 25% of the rooms at the Ramada Inn, in 35% of the rooms at the Sheraton, and in 40% of the rooms at the Lakeview Motor lodge, what is the probability that (a) a client will be assigned a room with faulty plumbing? (b) a person with a room having faulty plumbing was assigned accommodations at the Lakeview Motor Lodge? (c) a person with a room having no faulty plumbing was assigned accommodations at the Lakeview Motor Lodge? Round off the final answer to five decimal places.
A salon owner estimates the number of clients she is expecting during the festive season to be 20% during Monday to Wednesday, 20% on Thursday and 60% over the weekend. She therefore hires additional staff to assist during the weekend to meet the client demand. She however only observes 30% during Monday to Wednesday, 20% on Thursday and 50% over the weekend in the first week of December. The salon owner is uncertain whether she should reduce the planned staff for the December festive period due the observed trend or not. She conducts a statistical test at α = 0.05 to determine if the observed trend fits the expected trend. Which of the following statements is true? A. The conclusion of the test is that she should not keep the additional staff for the weekend. B. The df for this test is 3. C. The p-value is greater than α. D. The null hypothesis is that the observed trend is different to the expected trend. E. The test statistic is χ2 = 5.33.
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…
In a certain city, with a population of 1,000,000 people, 17 people have been infected with a disease. Five of these people are superspreaders. Superspreaders do not get sick, but will always be infected. Out of the remaining infected people, 50% do not get sick, and do not isolate, but will spread the disease for a week and then will no longer be infected. 35% will self-isolate and get better. The remaining 15% get sick and are admitted to hospital. Within a week, a superspreader will infect 0.1% of the population. A spreader is only infected for a week but will infect 0.01% of the population. Everyone in self-isolation will recover within a week. 50% of people in hospital will die, while the other 50% make a full recovery. a) Following this trend, what happens to the population over time?
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.

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