Question:

1. You are trying to develop a strategy for investing in two different development projects that will employ people in small towns in less developed countries. The anticipated annual return (in wages) to a small village for a $100,000 investment in each development under four different economic conditions has the following probability distribution: Returns ('0000 USD) Probability Economic Project A Project B condition 0.1 Recession - $50 -$100 0.3 Slow growth $20 $50 0.4 Moderate growth $100 $130 0.2 Fast growth $150 $200 a. Calculate the expected return for each project. b. Calculate the standard deviation of the return for each project c. Which project would you invest in? Why? 2. A brewery's experience is that one bottle per 10,000 bursts when filled. If filling each bottle is an independent trial, in a production run of 50000, what is the probability that fewer than 3 will burst? 3. A blood bank has scheduled 12 people to donate, and needs at least 5 donors for an open-heart surgery. The rate of no-shows is 25%, assumed independent. Find the probability that there will be insufficient blood for the surgery.4. The first year drop-out rate at a university is 23%. What is the probability that between 6 and 10 students (exclusive) will drop out from a beginning class of 45 entrants? 5. A photocopy repair firm's experience is that the number of calls per day for service is Poisson- distributed with a mean of 6. Find the probability of no more than 2 repair calls per day. 6. A bank experiences that the number of customers arriving in any hour is Poisson-distributed with a mean of 15. Find: a. the probability that 5 customers will arrive in an hour b. the probability that 25 customers will arrive in one hour. c. the probability that no more than 2 customers arrive in an hour d. the probability that more than 2 customers arrive in an hour