Complete the following probability distribution table: Probability Distribution Table X P(X) - 24 15 0.2 65 0.1 69 0.3The student counciL is hosting a drawing to raise money for scholarships. They are selling tickets for S10 each and will sell 500 tickets. There is one $2.000 grand prize, three S400 second prizes, and seventeen 530 third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent. Hint:_ Hint 1' _ Video on Expected Value 1' :+] Textbook prices have a seasonal structure on Ebay. At the end of a term, the supply of used books outstrips demand, and the price is lower. Near the start of a term, many students are looking for books, and the price is higher. Suppose we can classify sales for a particular chemistry textbook into these two time periods and an "other" time period in the proportions shown below. We have also listed the average price the textbook sells for in each of these three time periods Start-ofterm End-of-term Other 0.45 0.3 1 U. 24 $82.52 549.12 565.23 Sales proportion Average price For example, about 45% of Ebay auctions for this chemistry textbook occur at the start of the term and the books sell for an average of $82.52 during this time. Using the information above. compute the average price of the textbook over all seasons. [Do not put a dollar sign in your answer.) P(x) 0 0. 1 0.15 2 0.25 3 0.5 Find the mean of this probability distribution. Round your answer to one decimal place.13(3) 0.15 0.2 0.3 0.35 a. Find the expected value of the probability distribution. Round to two decimoi pieces. b. Find the standard deviation of the probability distribution. Round to two decimal places. A company estimates that 0.4.95 of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $100. If they offer a 2-year extended warranty for 515, what is the company's expected value of each warranty sold? Round your answer to the nearest cent. Suppose that you are offered the following "deal." You roll a six sided die. If you roll a I5, you win 510. If you rolL a 4 or 5, you win 55. Otherwise. you pay $10. a. Complete the PDF Table. List the X values, where X is the profit, from smallest to largest. Round to 4 decimal places where appropriate. Probability Distribution Table 3. Find the expected profit. 5 {Round to the nearest cent] c. Interpret the expected value. '32:.3'This is the most likely amount of money you will win. {:3 If you play many games you will likely lose on average very close to $1.67 per game. '12:? You will win this much if you play a game. d. Based on the expected value. should you play this game? '12:? No, since the expected value is negative. you would be very likely to come home with less money if you played many games. '12:? No, this is a gambling game and it is always a bad idea to gamble. '33::3'Yes, because you can win $10.00 which is greater than the 510.00 that you can Lose. '33::3'Yes, since the expected value is positive, you would be very likely to come home with more money if you played many games. '32:.3'Yes, since the expected value is 0. you would be very likely to come very close to breaking even if you played many games, so you might as well have fun at no cost. \fAssume that 12 jurors are randomly selected from a population in which 7996 of the people are Mexican- Americans. Refer to the probabiLity distribution table beLow and find the indicated probabiLities. :1: PM] 0 0+ 1 0+ 2 0+ 3 0.0001 4 0.000? 5 0.0044 I5 0.0193 ? 0.0621 8 0.146 9 0.2442 10 0.2?56 11 0.1885 12 0.0591 Find the probability of exactly IE: Mexican-Americans among 12 jurors. Round your answer to four decimal places. P(&: = 6] = Find the probability of 6 or fewer Mexican-Americans among 12 jurors. Round your answer to four decimal places. P($ g 6) 2 Does I5 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans? '12:? no 333' yes