1. A ski resort profits $1,200,000 during a good winter with lots of snow. The resort has a loss of $450,000 otherwise. The resort's historical climate data suggests that the probability of a good winter with lots of snow during any given year is 60%. What is the expected profit for the ski resort? Show significant work to justify answer.
Then explain what your answer really means. Is that how much you expect the ski resort to earn in one year? In two years? Is your answer the average profit over many years? Discuss the assumptions being made in the question.
2. The AB Company buys calculators from a Korean supplier. The probability of a defective calculator is 10%. If 3 calculators are selected at random, what is the probability that one of the calculators will be defective? Show work.
3. On a certain daily flight, Air Northeast has a policy of booking as many as 22 people on an airplane that can only seat 19. (Past studies have revealed that only 89% of the booked passengers actually arrive for the flight). Using the Binomial distribution, find the probability that if Air Northeast books 22 people on a flight, not enough seats will be available for all booked passengers.
4. The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams. If we select one box of cereal at random from this population, what is the probability that it will weigh less than 900 grams? Show work
5. An employer gives a pre-employment evaluation to a large group of applicants. The scores are normally distributed with a mean of 154 and a standard deviation of 21. The employer wants to interview only those applicants who score in the top 15%. What should the cut-off score be for the interviews? Round to nearest whole number. Show work
6. An employer wants to estimate to set a time limit so that 90% of the employees will finish a job on time. Past history has shown that the time required to do the job is normally distributed and has a mean time of 32 minutes with a standard deviation of 6 minutes. How much time should the employer allow employees to finish the job? Round to the nearest minute. Show work.
This solution calculates the average profit and basic probabilities of the scenarios in the question set. All workings are shown will formulas.