A city has just added 80 new female recruits to its police force. The city will provide a pension to each new hire who remains with the force until retirement. In addition, if the new hire is married at the time of her retirement, a second pension will be provided for her husband. A consulting actuary makes the following assumptions:(i) Each new recruit has a 0.37 probability of remaining with the police force until retirement.(ii) Given that a new recruit reaches retirement with the police force, the probability that she is not married at the time of retirement is 0.4.(iii) The number of pensions that the city will provide on behalf of each new hire is independent of the number of pensions it will provide on behalf of any other new hire.Determine the probability that the city will provide at most 54 pensions to the 80 new hires and their husbands. Enter your answer as a number accurate to 4 decimal places.[ ]

A city has just added 80 new female recruits to its police force. A consulting actuary makes the…

Answered: A city has just added 80 new female…

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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At a certain company, the mentoring program and the community outreach program meet at the same time, so it is impossible for an employee to do both. If the probability that an employee participates in the mentoring program is 0.43, and the probability that an employee participates in the outreach program is 0.32, what is the probability that an employee does the mentoring program or the community outreach program?
A local TV station employs Desmorelda, “Mistress of the Zodiac”, as its weather forecaster. She predicts a rainy day on the basis of Lunar phases. From statistical data (which is available to Desmorelda too) it is known that the probability of a rainy day during the Full Moon is 0,478, during the Third Quarter – 0,513, during the New Moon – 0,499, and during the First Quarter – 0,506. All phases last equally and the whole Lunar cycle takes 28 days. What is the probability that on a certain day Desmorelda will predict rain?
An insurance policy costs $120 and will pay policyholders $9,000 if they suffer a major injury (resulting in hospitalization) or $3000 if they suffer a minor injury (resulting in lost time from work). The company estimates that 1 in every 2088 policyholders will suffer a major injury and that 1 in 504 will suffer a minor injury. a) Create a probability model for the profit on a policy. b) What's the company's expected profit on the policy? c) What's the standard deviation? a) First find the probability and profit for each outcome. P(event) Profit no injury major injury minor injury (Round to six decimal places as needed.)
A city has just added 95 new female recruits to its police force. The city will provide a pension to each new hire who remains with the force until retirement. In addition, if the new hire is married at the time of her retirement, a second pension will be provided for her husband. A consulting actuary makes the following assumptions:(i) Each new recruit has a 0.4 probability of remaining with the police force until retirement.(ii) Given that a new recruit reaches retirement with the police force, the probability that she is not married at the time of retirement is 0.38.(iii) The number of pensions that the city will provide on behalf of each new hire is independent of the number of pensions it will provide on behalf of any other new hire.Determine the probability that the city will provide at most 69 pensions to the 95 new hires and their husbands. Enter your answer as a number accurate to 4 decimal places.
1. Researchers are interested in the relationship between vaping and upper respiratory infections. Suppose that 15% of their population of interest has vaped in the past year and 25% have had an upper respiratory infection in the past year. In addition, they know that 10% have both vaped and had an upper respiratory infection in the past year. What percent of the population has neither vaped nor had an upper respiratory infection in the past year? b. What is the probability of having an upper respiratory infection in the past year given that the person has vaped in the past year? What is the complement of the event in part b)? Be sure to interpret this probability in the context of the problem. a. C. d. What is the probability of having an upper respiratory infection in the past year given that the person has not vaped in the past year? Are the two events independent? Be sure to justify your answer. Based on your calculations what can you conclude about the relationship between vaping…
On any given morning here at Chabot College, coffee is brewed in the Science and Math Division workroom by one of two faculty members, depending on who arrives first at work. Instructor Yest arrives first 75% of the time. Instructor Kelly arrives first the remaining mornings. The probability that the coffee is brewed strong when brewed by Instructor Yest is 0.2. The probability that the coffee is brewed strong when brewed by Instructor Kelly is 0.9, as Instructor Kelly likes her coffee strong! Given the coffee is strong on a randomly selected morning, what is the probability that is was brewed by Instructor Yest?
Question 3: A package is being delivered to your home by one of the following shipping carriers: Postal Service, FedEx, or UPS. Suppose 40% of all packages are shipped by the Postal Service, 25% are shipped by FedEx, and 35% are shipped by UPS. The probability of the package being lost by these shipping carriers is 5%, 3%, and 7%, respectively. a) What is the probability that your package is lost? b) Given your package is lost, what is the probability that it was shipped by UPS?

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