(8) Every year, each employee at a large company must select one of two healthcare plans. It is expected that 15% ofthe employees currently using plan A will switch to plan B and that 25% of the employees currently using plan B willswitch to plan A. Out of the company's 1000 employees, 450 are currently enrolled in plan A.(a) Use a stochastic matrix to predict how many employees will be enrolled in each plan next year.(b) Use a stochastic matrix to predict how many employees will be enrolled in each plan in five years.

Answered: Image /qna-images/answer/d4b569a7-2445-4204-a550-6ac092ee3f6e.jpg

Answered: (8) Every year, each employee at a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A rainy year is 80% likely to be followed by a rainy year and a drought is 60% likely to be followed by another drought year. Suppose the rainfall condition is known for the initial year to be ‘rainy’. Then the vector ? 0 = 10 gives probabilities of rainy and drought for known initial year.(a) Write out the stochastic matrix.(b) Find the probabilities for:(i) Year 1(ii)
Suppose two companies, Company 1 and Company 2, are manufacturing a vaccineto treat COVID-19. Each company ships out 100 vaccines per shipment. A hospital is receiving40% of their vaccine shipments from Company 1 and the remainder of its vaccine shipmentsfrom Company 2. It is reported that from Company 1’s shipments, 7% of the vaccines getsdamaged in shipping meanwhile from Company 2’s shipments, 3% of the vaccines gets damagedin shipping. Suppose the hospital recently received a shipment of 100 vaccines but we are notsure if this shipment came from Company 1 or Company 2. Assuming that the vaccines areindependent of each other, what is the probability that exactly six vaccines in the shipment of100 are damaged?
A businessman is shipping a machine to another country. The cost of overhauling is $2700. If the machine fails in operation in the other country, it will cost $5500 in lost production and repairs. He estimates the probability that it will fail at 0.3 if it is not overhauled, and 0.2 if it is overhauled. Neglect the possibility that the machine might fail more than once in the 4 years (a) Prepare a payoff matrix. (b) What should the businessman do to minimize his expected costs? (a) Fill in the entries of the payoff matrix Fails Does Not Fail 8 81 (b) Would overhauling the machine before shipping minimize the businessman's expected costs? Overhaul Does Not Overhaul CETT OYes O No
Assume the chances of failure of each component is given in Figure. What is the probability that the system would not work? .
Two bicycle manufacturers, Alpha Cycles (A) and Best Bikes (B), buy parts from the suppliers Firm Frames (F), Great Gears (G) and Happy Handlebars (H). During the year 2019: 50% of the frames from Firm Frames (F) were sold to Alpha Cycles (A) and 50% were sold to Best Bikes (B). 75% of the gear sets from Great Gears (G) were sold to Alpha Cycles (A) and 25% were sold to Best Bikes (B). 40% of the handlebars from Happy Handlebars (H) were sold to Alpha Cycles (A) and 60% were sold to Best Bikes (B). Draw a network diagram with input nodes F, G and H, and output nodes A and B, that represents the proportion of parts sold from each supplier to each bicycle manufacturer Write down the matrix that represents this network. Use the matrix that you found to determine how many parts were sold to Alpha Cycles (A) during 2019, if the total number of parts sold to the two bicycle manufacturers by Firm Frames (F), Great Gears (G) and Happy Handlebars (H) was 240, 320 and 300 parts respectively.
In a survey, it was found that 72%of the population of a certain urban area lived in single-family dwellings and 28% in multiple housing. One year later, of those who had been living in single-family dwellings, 89%still did so, but 11% had moved to multiple-family dwellings. Of those in multiple housing, 94%were still living in that type of housing, while 6%had moved to single-family housing. Assume that these trends continue. (a) Write a transition matrix using this information. Set it up so that the first row and first column represent single-family dwellings and the second row and second column represent multiple housing.
Either a mixed column or mixed row strategy is given. Use the given payoff matrix and find the optimal pure strategy (or strategies) the other player should use. Express the answer as a row or column matrix. Also determine the resulting expected payoff.
1
In an office complex of 1000 employees, on any given day some are at work and the rest are absent. It is known that if an employee is at work today, there is an 85% chance that she will be at work tomorrow, and if the employee is absent today, there is a 70% chance that she will be absent tomorrow. Suppose that today there are 740 employees at work. (A graphing calculator is recommended.) (a) Find the transition matrix A for this scenario. at work absent A = (b) Predict the number that will be at work five days from now. (Round your answer to the nearest integer.) employees (c) Find the steady-state vector x. (Round your answer to two decimal places.)
↑ The 1990 census reported that 32% of the households in Middletown were homeowners and the remainder were renters. During the next decade, 10% of the homeowners became rent and the rest continued to be homeowners. Similarly, 14% of the renters became homeowners and the rest continued to rent (A) Fill in the appropriate transition matrix for this process. Homeowners Homeowners Renters Renters AR NE
Explain, in your own words: What is the purpose of a control matrix?
In any given day the air quality in a certain city is either good or bad. Records show that when the air quality is good on one day, then there is a 95% chance that it will be good the next day, and when the air quality is bad on one day, then there is 45% chance it will be bad the next day. a. Give the transition matrix. b. if the air quality is good today, what is the probability it will be good two days from now? c. if the air quality is bad today, what is the probability it will be bad three days from now? d. if the there is 20% chance the air quality is good today, what is the probability it will be good tomorrow?

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