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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- An insurance company would like to offer theft insurance for renters. The policy wouldpay the full replacement value of any items that were stolen from the apartment. Someapartments have security alarms installed. Such systems detect a break-in and ring an alarmwithin the apartment. The insurance company estimates that the probability of a theft in ayear is .05 if there is no security system and .01 if there is a security system (there cannot bemore than one theft in any year). An apartment with a security system costs the renter anadditional £50 per year. Assume that the loss from a theft is £10,000 and that the insurancecompany is risk neutral and the renter would be willing to pay more than the expected loss toinsure against the loss of theft. What is the insurance company's break even price for a one year theft insurance policy for anapartment without a security system?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?Suppose the market for auto insurance is made of up two types of buyers: high-risk and low-risk. Buyers’ willingness to pay (WTP) for auto insurance plans, and sellers’ willingness to accept (WTA) when selling plans to each type of buyer, are outlined in a photo Assume now that there is asymmetric information and that insurance companies do not knowhow risky an individual buyer is. In the face of this uncertainty, they determine that the probability that a “walk-in” is high-risk is 0.75. What is the minimum price sellers are willing to accept when selling aninsurance plan? At this price, will low- and high-risk buyers both be willing to purchase this insurance plan? Explain. Be sure the mention adverse selection in your answer. Returning to the conditions outlined in Q1, suppose that buyers of auto insurance (high- and low-risk) were offered a $1,000 subsidy to purchase coverage. This would raise their WTP by $1,000. Would the market for both insurance plans clear after the…
- In the game of blackjack as played in casinos in Las Vegas, Atlantic City, and Niagara Falls, as well as in many other cities, the dealer has the advantage. Most players do not play very well. As a result, the probability that the average player wins a hand is about 45%. Find the probability that an average player wins. a.Twice in 5 hands. b. Ten or more times in 25 hands. Arrivals 0 1 2 3 4 5 6 7 8 Frequency 14 31 47 41 29 21 10 5 2The owner of a firm must hire a manager to launch a new product. The new product can be successful and generate a revenue of 5000 or fail and generate a revenue of 1000. The probability of succ success is 0.7 (and hence the probability of failure is 0.3). If the manager exerts low effort (e=e,) then the probability of success is 0.2 (and hence the probability of failure is 0.8). The manager's utility effort chosen by the manager, with D(e) = 10 and D(e)-o. The manager's reservation utility is -40 The wage paid by the owner to the manager is the owner's only cost. The owner is risk neutral. If the owner could observe the manager's effort and would want the manager to exert high effort, what contract would he offer to the manager? What is the own Assume from now on that the manager's effort is unobservable. Suppose that the owner still wants to ensure that the manager accepts the proposed contract an this to happen. c) a)? a) b) It can be shown that the constraints in point b) must be…A market research firm is interested in surveying certain attitudes in a small community. There are 125 households broken down according to income, ownership of a telephone or ownership of a T.V. Household with monthly Household with monthly 8.000 income of " 8,000 or less Telephone Subscriber income above No Telephone Telephone SubsNcriber No. Telephone Own 7V. set 27 20 18 10 No. T.V. set 18 10 12 10 (i) What is the probability of obtaining of a TV. owner in drawing at random ? (ii) If a household has monthly income over Rs. 8,000 and is a telephone subscriber, what is the probability that it has a T.V. ? (iii) What is the conditional probability of drawing a household that owns a T.V., given that the household is a telephone subscriber ? (iv) Are the events 'ownership of a T.V.' and 'telephone subscriber statistically independent ? Comment.
- Suppose that the distribution of Uber rides around the quoted arrival time is normally distributed. Themean waiting time (relative to the quoted time) is 0, with a standard deviation of 3 minutes.a. Using the empirical rule, what percentage of rides arrive within 3 minutes of the mean (3 minutesbefore to 3 minutes after)?b. Graphically depict the area that would need to be calculated to determine the probability ofwaiting more than 4 minutes for a ride. Explain your graph.In a tight real estate market, the probability that a buyer's offer will be accepted is 0.50 if she bids more than 15 thousand above the asking price. The probability of acceptance drops to 0.20 if she bids below this amount. Overall, sixty percent of offers are more than 15 thousand above the asking price. The probability that a randomly selected offer will be accepted by the seller is closest or equal to: 0.15 0.38 0.20 0.32 O 0.18Exercise 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.
- 5.100 Tossing a die. You are tossing a balanced die that has probability 1/6 of coming up 1 on each toss. Tosses are independent. We are interested in how long we must wait to get the first 1. (a) The probability of a 1 on the first toss is 1/6. What is the probability that the first toss is not a 1 and the second toss is a 1? (b) What is the probability that the first two tosses are not 1s and the third toss is a 1? This is the probability that the first 1 occurs on the third toss. 4 (c) Now you see the pattern. What is the probability that the first 1 occurs on the fourth toss? On the fifth toss?Suppose that a family has 4 chilidren. Also, suppose that the probability of having a boy is Find the probability that the family has at least 3 boys. The probability that the family has at least 3 boys is (Type an integer or a simplified fraction,)Two factories mamufacture the Number of Defects same machine parts. Each part is classified as having either 0, 1, 2 or 3 mamufacturing defects. The joint probability for this is given in the adjoining Table. (i) A part is observed to have no defect. What is the probability that it was produced by X mamufacturer ? Manufacturer 21 3 0-1250 0-0625 0-1875 0-1250 Y 0-0625 0-0625 0-1250 0-2500 (ii) A part is known to have been produced by mamufacturer X. What is the probability that the part has no defects ? (iii) A part is known to have two or more defects. What is the probability that it was manufactured by X? (iv) A part is known to have one or more defects. What is the probability that it was manufactured by Y ?