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Of a group of patients having injuries, 28% visit both a physical therapist and a chiropractor while 8% visit neither. Say that the

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- Please answer number 17arrow_forwardHW Score: 80%, ○ Points: 0 of Save 10 According to an article, 41% of all cars crossing a toll bridge have a commuter sticker. What is the probability that among 100 randomly selected cars waiting to cross the bridge, at most 30 have commuter stickers? The probability that at most 30 cars have commuter stickers is ☐ (Round to four decimal places as needed.) More Vo Vi (0,0)arrow_forwardA telegraph can transmit two different signals: a dot and a dash. We want to encode the 26 letters of the Englishalphabet and the ten digits 0, 1, 2, . . . , 9 using sequences of these two symbols. What is the smallest integer n suchthat we can encode all these letters and digits with sequences of length at most n and length at least 1?arrow_forward
- We roll seven 20-sided dice, numbered 1 to 20. Show that it is always possible to find two disjoint nonempty subsetsof the dice such that the sums of the shown faces of the dice in each of the subsets coincide.arrow_forwardAnswer this two questions: 2 . We roll seven 20-sided dice, numbered 1 to 20. Show that it is always possible to find two disjoint nonempty subsets of the dice such that the sums of the shown faces of the dice in each of the subsets coincide(only one of the faces is considered to be shown) . 4. We are given a deck of 60 cards, 40 are identical black cards, 10 are identical red cards, and 10 are identical greenc ards. How may ways are there to deal the 60 cards to three distinct players so that everyone gets exactly 20 cards?arrow_forward3. A room has a large circular table with ten seats, numbered 1 to 10, such that to the right of seat number i is seat number i + 1 for all i ∈ {1, . . . , 9} and to the right of seat 10 is seat 1. We want to assign seats to 10 people, 6 of them only speak Slovene, 1 of them only speaks English, and the remaining 3 speak both Slovene and English, by giving out numbered place cards. In how many ways can we do that so that everyone sits next to at least one person who speaks a common language?arrow_forward
- 1. A telegraph can transmit two different signals: a dot and a dash. We want to encode the 26 letters of the English alphabet and the ten digits 0, 1, 2, . . . , 9 using sequences of these two symbols. What is the smallest integer n such that we can encode all these letters and digits with sequences of length at most n and length at least 1?arrow_forwardCalculating probability for the Standard Normal Curve 1. Assume the mean is zero, the standard deviation is one, and it is associated with the distribution of z values. Each problem is worth 2 points, 1 point for drawing out the curve and shading the area requested and 1 point for the answer. a. What is the P(z > 0)? b. What is the P(z < 1.0)? C. What is the P(z <-1.0)?arrow_forwardStarting with the finished version of Example 6.2, attached, change the decision criterion to "maximize expected utility," using an exponential utility function with risk tolerance $5,000,000. Display certainty equivalents on the tree. a. Keep doubling the risk tolerance until the company's best strategy is the same as with the EMV criterion—continue with development and then market if successful. The risk tolerance must reach $ 160,000,000 before the risk averse company acts the same as the EMV-maximizing company. b. With a risk tolerance of $320,000,000, the company views the optimal strategy as equivalent to receiving a sure $____________ , even though the EMV from the original strategy (with no risk tolerance) is $ 59,200.arrow_forward
- Starting with the finished version of Example 6.2, attached, change the decision criterion to "maximize expected utility," using an exponential utility function with risk tolerance $5,000,000. Display certainty equivalents on the tree. a. Keep doubling the risk tolerance until the company's best strategy is the same as with the EMV criterion—continue with development and then market if successful. The risk tolerance must reach $ ____________ before the risk averse company acts the same as the EMV-maximizing company. b. With a risk tolerance of $320,000,000, the company views the optimal strategy as equivalent to receiving a sure $____________ , even though the EMV from the original strategy (with no risk tolerance) is $ ___________ .arrow_forwardA television network earns an average of $14 million each season from a hit program and loses an average of $8 million each season on a program that turns out to be a flop. Of all programs picked up by this network in recent years, 25% turn out to be hits and 75% turn out to be flops. At a cost of C dollars, a market research firm will analyze a pilot episode of a prospective program and issue a report predicting whether the given program will end up being a hit. If the program is actually going to be a hit, there is a 75% chance that the market researchers will predict the program to be a hit. If the program is actually going to be a flop, there is only a 30% chance that the market researchers will predict the program to be a hit. What is the maximum value of C that the network should be willing to pay the market research firm? Enter your answer in dollars, not in million dollars. $ __________ Calculate EVPI for this decision problem. Enter your answer in dollars, not in million…arrow_forwardTwo construction companies are bidding against one another for the right to construct a new community center building. The first construction company, Fine Line Homes, believes that its competitor, Buffalo Valley Construction, will place a bid for this project according to the distribution shown in this table: Buffalo Valley's Bid Bid Probability $160,000 0.2 $165,000 0.5 $170,000 0.2 $175,000 0.1 Furthermore, Fine Line Homes estimates that it will cost $160,000 for its own company to construct this building. Given its fine reputation and long-standing service within the local community, Fine Line Homes believes that it will likely be awarded the project in the event that it and Buffalo Valley Construction submit exactly the same bids. Find the bid that maximizes Fine Line’s expected profit. Max expected profit $ ________ . Bid that maximizes profit $ ________ .arrow_forward
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