Two types of light bulbs are manufactured by firm A and firm B. The life of bulb type A is normally distributed with mean 100 hours and variance 15. The life of bulb type B is normally distributed with mean 105 hours and variance 30. (i) What is the probability that a type A bulb will last more than 110 hours? (ii) If 20 bulbs each of type A and type B bulbs are turned on at the same time, what is the probability that type A bulbs will last longer than type B bulbs ?
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- 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?2.4 The opening 2018 World Cup odds against being the winning team specified by espn.com were 9/2 for Germany, 5/1 for Brazil, 11/2 for France, 20/1 for England, and 7/1 for Spain. Find the corresponding prior probabilities of winning for these five teams.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!
- Using the standard normal distribution table, compute the following probabilities P(Z ≥1.92) is:You have drawn a painting that you want to sell to an anonymous buyer, but you do not know exactly how much they are willing to pay. Based on past experiences, you estimate that the buyer will be willing to pay in monetary units where a random variable is evenly distributed continuously over the interval [200, 500]. Let's assume that your assessment regarding the random variable is correct, i.e., that it is indeed evenly distributed continuously over the interval [200, 500]. What price �p will you choose if you want to maximize your expected profit? What will be your expected profit?A mutual fund company has 6 funds that invest in the U.S. market and 4 that invest in international markets. A customer wants to invest in two U.S. funds and 2 international funds.a. How many different sets of funds from this company could the investor choose?b. Unknown to this investor, one of the U.S. funds and one of the international funds will seriously underperform next year. If the investor selects funds for purchase at random, what is the probability that at least one of the chosen funds will seriously underperform next year?
- If patient insurance inquiries arrive at Blue Choice insurance with a mean rate of 3.6 calls per minute, the exponential probability of waiting more than 0.5 minutes to get the next inquiry call is _____. Question 6Select one: a. 0.2407 b. 0.1222 c. 0.5000 d. 0.1653Please do not give solution in image format thanku Two Manufacturers supply food to a large cafeteria. Manufacturer A supplies 40% of the soup served in the cafeteria, while Manufacturer B supplies 60% of the soup that is served. 3% of the soup cans provided by Manufacturer A are found to be dented, while 1% of the cans provided by Manufacturer B are found to be dented. Given that a can of soup is dented, find the probability that it came from Manufacturer B.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?
- "Jay, a writer of novels, just has completed a new thriller novel. A movie company and a TV network both want exclusive rights to market his new title. If he signs with the network, he will receive a single lump sum of $1,480,000, but if he signs with the movie company, the amount he will receive depends on how successful the movie is at the box office.The probability of a small box office earning $203,000 is 0.27. The probability of a medium box office of $1,660,000 is 0.49, and the probability of a large box office of $2,950,000 is 0.24.Jay can send his novel to a prominent movie critic to assess the potential box office success. It will cost $20,000 to get the novel evaluated by the movie critic.The movie critic can have either a favorable or unfavorable opinion. The movie critic's reliability of predicting box office success is as follows.If the movie will have a large box office, there is a 0.75 probability the critic will have a favorable opinion.If the movie will have a medium…Your company has a customer list that includes 3000 people. Your market research indicates that 90 of them responded to the coupon. If you send a coupon to ONE customer at random, what’s the probability that he or she will use the coupon? Group of answer choices 3%. 9%. 30%. 90%. None of the above.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.