A. A survey of 200 retail grocery shops revealed the following monthly income pattern: Monthly Income Under k20,000 K20,000 to k30,000 k30,000 and above Number of shops 102 61 37 (i) What is the probability that a particular shop has a monthly income under k20,000? (ii) What is the probability that a selected shop at random has either an
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- Refer to Table 3.10.What is the joint probability of “low income” and “regular”?A production manager knows that 5% of components produced by a particular manufacturing process have some defect. Six of these components, whose characteristics can be assumed to be independent of each other, are examined.a. What is the probability that none of these components has a defect?b. What is the probability that one of these components has a defect?c. What is the probability that at least two of these components have a defect?Suppose that there are two types of workers: high and low. Employers cannot distinguish between different types during an interview. Employers value high type at $200,000 and low type at $100,000. Employers are in a competitive market (i.e. zero profit applies). High type workers have a reservation wage of 140,000 and low type workers have a reservation wage of 80,000. Suppose that 50% of all workers are high type. The productivities, reservation wages, and the probabilities are common knowledge). What wage would the employers offer? Please explain the solution!
- Early in August an undergraduate college discovers that it can accommodate a few extra students. Enrolling those additional students would provide a substantial increase in revenue without increasing the operating costs of the college; that is, no new classes would have to be added. From past experience the college knows that the frequency of enrollment given admission for all students is 40%.a. What is the probability that at most 6 students will enroll if the college offers admission to 10 more students?b. What is the probability that more than 12 will actually enroll if admission is offered to 20 students?c. If the frequency of enrollment given admission for all students was 70%, what is the probability that at least 12 out of 15 students will actually enroll?Avicenna is a major insurer that offers five-year life insurance policies to 65 year-olds. If the holder of one of these policies dies before the age of 70 years, the company must pay $213,000 the beneficiary of the policy. Avicena executives are considering the possibility of offering these policies to $9,380 each one. Suppose there is a 4% probability that the insured will die before the 70 age of years and a 96% probability that she will live to 70 age.If Avicena executives know they will sell many of these policies, should they expect to make or lose money by offering them? How much would they win or lose?To respond, take into account the price of the policy and the expected value of the amount paid to the beneficiary.Find the probability that there are three H when a fair coin is flipped four times. ___________% (Round the answer to 2 decimal points.)
- What is the probability of P(Z< -1.07)The probability that the next President will be a Democrat is 0.5, and the probability that the next President will be a woman is 0.3. The probability the next President will be a woman and a Democrat is 0.1. What is the probability the next President will be a Democrat or a woman?On Monday's there are eight classes taught in the business building. The probability that any of those classes starts late is 0.3. What is the probability that at least one these classes will start late on Monday?
- When a pair of dice is tossed, the results may be any whole number from 2 through 12. In the game of craps one can win by tossing either a 7 or an 11 on the first roll. What is the probability of doing this?The owner of Tastee Cookies needs to decide whether to lease a small, medium, or large new retail outlet. She estimates that monthly profits will vary with demand for her cookies as follows: SIZE OFOUTLET DEMAND LOW HIGH Small $ 1,000 1,000 Medium 500 2,500 Large 0 3,000 For what range of probability that demand will be high, will she decide to lease the medium facility?Question 2An investor is to purchase one of three types of real estate, as illustrated inFigure below. The investor must decide among an apartment building, anoffice building, and a warehouse. The future states of nature that willdetermine how much profit the investor will make are good economicconditions and poor economic conditions. The profits that will result fromeach decision in the event of each state of nature are shown in Table below: Assume that it is now possible to estimate a probability of 0.60 that goodeconomic conditions will exist and a probability of .40 that poor economicconditions will exist. a) Determine the best decision by using expected opportunity loss. b) Develop a decision tree, with expected values at the probability nodes. c) Compute the expected value of perfect information.