MATH+125+10

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Apr 30, 2024

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10.6 Expected Value Define Random Variable: Example 10.6.1 (Calculating Expected Value): Figure 10.6.1 shows a wheel used in a carnival game at a children’s party where a player spins and wins the amount of candy the wheel lands on. Table 10.6.1 lists the possible outcomes along with their respective probabilities for the wheel. a. Use the wheel to determine the expected number of pieces of candy each player wins.
Example 10.6.1 (Calculating Expected Value): Figure 10.6.1 shows a wheel used in a carnival game at a children’s party where a player spins and wins the amount of candy the wheel lands on. Table 10.6.1 lists the possible outcomes along with their respective probabilities for the wheel. b. The host of the party does not want to run out of candy. If 15 children each play the game 5 times, how many pieces of candy should the host expect to give out? c. What are the maximum and minimum amounts of candy that the host should expect to hand out at this game? Skill Check 10.6.1: Given the following table of outcomes of an event and their respective probabilities, complete the table and then determine the expected value of the event.
Example 10.6.2 (Calculating Expected Value): The campus dining service at State University is preparing for the fall semester. Based on past years, they have observed the following data on the probability of selling different meal plans. Each plan consists of a set number of meals along with Plus Dollars, which can be used anywhere on campus but are restricted to food purchases. The university predicts an enrollment of 8421 students in the fall semester. Use Table 10.6.4 to answer questions a through c. a. On average, how much does one student spend on a meal plan for the fall semester? b. Suppose that, for each meal plan sold, the university makes $510 from Plan 1, $550 from Plan 2, $600 from Plan 3, $220 from Plan 4, and $270 from Plan 5. What is the expected profit per student for dining services in the upcoming semester? c. What overall profit can dining services expect from student meal plans in the upcoming semester?
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