Have you ever played rock-paper-scissors (or rochambeau)? it's considered a "fair game" in that the two players are equally likely to win (like a coin toss). both players simultaneously display one of three hand gestures (rock, paper, or scissors), and the objective is to display a gesture that defeats that of your opponent. the main gist is that rocks break scissors, scissors cut paper, and paper covers rock. we investigated some results of the game rock-paper-scissors, the researchers had 119 people play rock paper- scissors against a computer. they found 66 players (55.5%) started with rock, 39 (32.8%) started with paper, and 14 (11.8%) started with scissors. we want to see if players start with rock with a probability that is different from 1/3.

Autility company burns coal to generate electricity. the cost c(p), (in dollars) of removing p percent of the some stack pollutants is given by c(p)= 85000p/100-p a) find the cost to remove 30% of the pollutant b) find where the function is undefined

In tossing one coin 10 times, what are your chances for tossing a head? a tail? 2. in tossing one coin 100 times, what are your chances for tossing a head? a tail? 3. in tossing one coin 200 times, what are your chances for tossing a head? a tail? deviation = ((absolute value of the difference between expected heads and observed heads) + (absolute value of the difference between expected tails and observed tails)) divided by total number of tosses. this value should always be positive. 4. what is the deviation for 10 tosses? 5. what is the deviation for the 100 tosses? 6. what is the deviation for 200 tosses? 7. how does increasing the total number of coin tosses from 10 to 100 affect the deviation? 8. how does increasing the total number of tosses from 100 to 200 affect the deviation? 9. what two important probability principles were established in this exercise? 10. the percent of occurrence is the obtained results divided by the total tosses and multiplied by 100%. toss the coins 100 times and record your results. calculate the percent occurrence for each combination. percent head-head occurrence: percent tail-tail occurrence: percent head-tail occurrence:

3.17 scores on stats final. below are final exam scores of 20 introductory statistics students. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 57, 66, 69, 71, 72, 73, 74, 77, 78, 78, 79, 79, 81, 81, 82, 83, 83, 88, 89, 94 (a) the mean score is 77.7 points. with a standard deviation of 8.44 points. use this information to determine if the scores approximately follow the 68-95-99.7% rule. (b) do these data appear to follow a normal distribution? explain your reasoning using the graphs provided below.