1. A certain game involves tossing 3 fair coins, and it pays 10 cents for 3 heads, 5 cents for 2 heads, and 3 cents for 1 head. Is 5 cents a fair price to pay to play this game? That is, does the 5 cents cost to play make the game fair? Show work. 2. An insurance company will insure a $200,000 dollar home for its total value for an annual premium of $650. If the company spends $25 per year to service such a policy, the probability of total loss for such a home in a given year is 0.002, and you assume that either total loss or no loss will occur, what is the company's expected annual gain (or profit) on each such policy? Show work. 3. Five thousand raffle tickets are sold. One first prize of $1000, two second prizes of $500 each, and three third prizes of $100 each will be awarded, with all winners selected randomly. If you purchased one ticket, what are your expected gross winnings? 4. Four cards are numbered 1 through 4. Two of these cards are chosen randomly without replacement, and the numbers on them are added. Find the expected value of this sum. 5. Lori, a commercial building contractor, will commit her company to one of three projects, depending on her analysis of potential profits or losses as shown here. (See chart on attached picture of lined paper below spinners) Determine which project Lori should choose according to each approach. Expected values The optimist viewpoint The pessimist viewpoint 6. David, the promoter of an outdoor concert, expects a gate profit of $100,000 unless it rains, which would reduce the gate profit to $30,000. The probability of rain is 0.20. For a premium of $25,000 David can purchase insurance coverage that would pay him $100,000 in case of rain. Find the expected net profit when the insurance is purchased Find the expected net profit when the insurance is not purchased 1. The following raw data represent the monthly account balances for a sample of 50 brand new charge card users. 78 175 46 138 79 118 90 163 88 107 126 154 85 60 42 54 62 128 114 73 67 119 116 145 129 130 81 105 96 71 100 145 117 60 125 130 94 88 136 112 85 165 118 84 74 62 81 110 108 71 Use seven classes with a uniform width of 20 dollars where the lower limit of the first class is 40 dollars. Construct grouped frequency and relative frequency distributions in a table. Construct a histogram Construct a frequency polygon 2. The following data represent net yards gained per game by National Football League running backs who played during a given week of the season. 25 19 65 52 19 39 43 29 36 45 33 18 73 22 55 25 37 58 40 41 88 7 29 3 67 33 54 123 73 30 43 24 112 60 94 86 49 102 16 32 79 36 62 46 Create a stem-and-leaf plot for the given data. Treat the one digits as the leaves. For any single-digit data, use a stem of 0. 3. Data for a recent year showed that the average annual earnings of American workers corresponded to educational level as shown in the table below. Draw a bar graph that shows this information. Educational Level Less than a high school diploma High school graduate Some college, no degree Associate degree Bachelor's degree Masters degree Professional degree Doctoral degree Median Weekly Earnings $453 $618 $699 $757 $1012 $1233 $1531 $1561 1. For each list of data, calculate (a) the mean, (b) the median, and (c) the mode or modes 3.1, 4.5, 6.2, 7.1, 4.5, 3.8, 6.2, 6.3 2. The average of 5 quiz grades is 10. When the lowest grade is dropped and the new average is calculated, it turns out to be 11. What was the score fo the dropped grade? Show work. 3 & 4. The table shows the top five U.S. businesses, ranked by 2012 revenue. Business Revenue (in billions) Profit (in billions) Walmart $469.2 ExxonMobil $449.9 Chevron $233.9 Phillips 66 $169.6 Berkshire Hathaway $162.5 $17.0 $44.9 $26.2 $4.1 $14.8 Find each of the following quantities for these five businesses. The mean revenue The median profit 5. While doing an experiment, a physics student recorded the following sequence of elapsed time (in seconds) in a lab notebook. 2.16, 22.2, 2.96, 2.20, 2.73, 2.28, 2.39 When reviewing the calculations later, he decided that the entry 22.2 should have been recorded as 2.22 and made that change in the listing. In general, which measure, mean or median, is affected less by the presence of an extreme value in the data? 6. For each of the following frequency distributions, find (a) the mean (to nearest tenth), (b) the median, and (c) the mode or modes (if any) Value 615 540 605 579 586 600 Frequency 13 7 9 14 7 5 \fProject A A continued Project B B continued Project C C continued Profit or loss (x) Probability P (x) Profit or loss (x) Probability P (x) Profit or loss (x) Probability P (x) $60,000 0.10 $0 0.20 $40,000 0.65 $180,000 0.60 $210,000 0.35 $340,000 0.35 $250,000 0.30 $290,000 0.45