The probabilities of X, Y and Z becoming managers are 4/9, 2/9 and 1/3 respectively. The probabilities that the Bonus Scheme will be introduced if X, Y and Z becomes managers are 3/10, 1/2, and 4/5 respectively. (i) What is the probability that Bonus Scheme will be introduced, and (ii) if the Bonus Scheme has been introduced, what is the probability that the manager appointed was X ?
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- A signed a contract with B to buy a machine at a price of $920. Assume that A's value for the machine is $1000. At the time when the contract is signed, B's cost of making the machine is a random variable subject to the following probability distribution. Realized Cost Probability 1200 800 400 0.3 0.5 0.2 What is the efficient probability that the contract is breached?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?21 Los Angeles averages 266.5 sunny days per year. What is probability that Boston has at least as many sunny days as Los Angeles? a 0.0020 b 0.0031 c 0.0047 d 0.0073
- Please no written by hand solution Kate recently invested in real estate with the intention of selling the property one year from today. She has modeled the returns on that investment based on three economic scenarios. She believes that if the economy stays healthy, then her investment will generate a 30 percent return. However, if the economy softens, as predicted, the return will be 10 percent, while the return will be -25 percent if the economy slips into a recession. If the probabilities of the healthy, soft, and recessionary states are 0.6, 0.2, and 0.2, respectively, then what are the expected return and the standard deviation of the return on Kate❝s investment? Calculate the coefficient of variation for this investment. (Round expected return to 3 decimal places, e.g. 0.125 and round intermediate calculations and standard deviation to 5 decimal places, e.g. 0.07680.)a) Grace Floral Shop sells several types of roses for all occasions. It is known that 43% of the roses that is sold by Grace Floral Shop are Eden Roses. 12 roses are ordered to put in a bouquet (i) Define the random variable for this situation and list its values (ii) Stating its parameter(s), what is the probability distribution of this variable? (iii)State the conditions that influence your choice of distribution. (iv)Calculate the probability that at most 2 of the roses were Eden Roses. b) The number of telephone calls coming into Grace Floral Shop to place orders averages 3 per minute. (i) Define the random variable in this situation and list its values. (ii) Stating its parameter(s), what is the probability distribution of this variable? (iii)Compute the probability that 5 calls will arrive per minute. (iv)Compute the probability that 3 or more calls will arrive in a 3-minute interval?The probability distribution for the number of automobiles sold during a day (x) at Bob Iron Motors isas follows. x f(x) 0 0.001 1 0.007 2 0.034 3 0.099 4 0.188 5 6 0.220 7 0.136 8 0.055 9 0.015 10 0.001 17 The probability that 5 automobiles will be sold is,a 0.232b 0.244c 0.257d 0.271
- a) There is small parking lot behind a Floral Shop that has two parking lot spaces. Let X be the number of cars parked in the parking lot at midday. The probability distribution of X is given by x 0 2 3 P(X = x) 0.1 0.25 a 0.35 (i) What is the value of a? (ii) (iii) What is the probability that there will be at most 1 car in the parking lot? Calculate the expected number of cars in the parking lot at midday (iv) Calculate the variance.Guy Fieri has purchased a significant plot of land in Northwest Ohio for his newest venture: FlavorTownship. This hub for mind-boggling flavor and entertainment is a strictly for-profit operation. Guy would like to keep Flavor Township open all year-round, but due to Ohio weather the following are the probabilities of when it will be open: |- 30% chance it is open 300 days a year |- 55% chance it is open 325 days a year |- 15% chance it is open 350 days a year Flavor Township will expect to host 14,000 people each day that it is open and expects an average revenue of $45 per visitor. This paradigm-shifting landmark will cost $420,000,000 to start the investment and will require annual costs (food, employees, etc.) of $115,000,000. Every 3 years, Flavor Township will undergo necessary maintenance that will cost $22,000,000. If the expected life of Flavor Township is 15 years and a 16% return is expected, what is the expected NPV of this project?Marcus is an expected utility maximizer with the Bernoulli utility function u(w) = √w. He faces a gamble in his wealth. In a good state he gets 81 and in a bad state he gets 9. He can take out an insurance plan which will leave him with a wealth of 49 in each state. (a) (b) (c) state? Is Marcus risk averse? Will he purchase the insurance if the probability of the states is ½ for each Let p denote the probability of the good state. For what value(s) of p will Markus be just indifferent between taking out the insurance and not taking it out? Show your working.
- Question 3 a) Grace Floral Shop sells several types of roses for all occasions. It is known that 43% of (i) (ii) (iii) the roses that is sold by Grace Floral Shop are Eden Roses. 12 roses are ordered to put in a bouquet Stating its parameter(s), what is the probability distribution of this variable? State the conditions that influence your choice of distribution. Calculate the probability that at most 2 of the roses were Eden Roses. b) The number of telephone calls coming into Grace Floral Shop to place orders averages 3 per minute. (i) (ii) Stating its parameter(s), what is the probability distribution of this variable? Compute the probability that 5 calls will arrive per minute. (iii) Compute the probability that 3 or more calls will arrive in a 3-minute interval?An investor with initial wealth W is given the opportunity to invest in a start-up (1) company. If the company does well, the investor will make a 200% profit in her investment, but if the company fails, the investor will lose all her investment. That is, if the investor invests X, she will get back 3x if the company succeeds and nothing if the company fails. The company will fail with probability 1/2 and will succeed with probability 1/2. The investor is risk-averse and has utility function u(x) wealth W should she invest in this company? Vx. What fraction of her initialExercise 15:- Each unit of a product produced and sold earns a profit of Rs. 50 and unsold units result into a loss of Rs. 30. The probability distribution is given below :Units Demanded : 0 1 2. 3.Probability : 0.2. 0.2. 0.25. 0.3Calculate EPPI and EVPI.