Suppose a person is thinking about entering a MarioKart competition at their local videogame store. The competition costs 20 dollars to enter. The competition consists of 10 matches. The person knows that their chance of winning each match is 65% and that each match is independent of the others. The payout for the competition is: WIN ALL 10 Matches: 500 Dollar Prize WIN 9 Matches: 250 Dollar Prize WIN 8 Matches: 50 Dollar Prize OTHERWISE: Nothing 1) Suppose that this person enters the competition 5 times. What is the probability they break even? (Hint: To break even they would need to win the $50 prize twice and lose the other three times. Use a modified binomial to calculate this probability

Joe and Maggie take turns mowing the lawn each week.  Maggie suggests they try a new system for determining who should mow the lawn.  Each week, they will roll two dice and determine the sum of the values.  Since the highest possible sum is 12, Maggie will mow the lawn if the sum is 6 or less, and Joe will mow the lawn if the sum is greater than 6. Before agreeing to Maggie's suggestion, Joe wants to check if this plan would be fair.  He decides to roll a pair of dice and determine the sum of the values 100 times.  The graph shows the results of the 100 trials. Based on his simulation, should Joe agree to Maggie’s plan?   (yes/no), because a sum greater than 6 is likely to occur (more than, less then, equal to)(30%, 50%, 75%) of the time

You randomly recruit 23 students and tell each of them to come to the lab in two different mornings: each morning they will be offered some breakfast and will take a test. Each student will receive the light breakfast one time and the nutritious breakfast the other time (some will receive the light breakfast first, the others will receive the nutritious breakfast first, and the second time they switch). The average difference in a student’s score after eating the nutritious breakfast and their score after eating a light breakfast is 4.5, and the standard deviation of this difference is 3.6. (a)  Construct a 95% confidence interval for the difference in the average score of students after having a nutritious breakfast and the average score of students after having a light breakfast.

B. Perimeter Shot - A perimeter shot, also known as a mid-range shot, is a jump shot or general field goal attempt that an offensive player can take inside of the three-point line and is worth 2 points. To practice this, Piel has to choose four different shooting spots among the five different spots in where he is comfortable of shooting. In previous games, his shot selection is 5% from the right baseline (Spot 1), 15% from the right elbow (Spot 2), 20% from the top of the key (Spot 3), 25% from the left elbow (Spot 4) and 35% from the left baseline (Spot 5). In this drill, a shooting spot can be selected once, multiple times, or not at all. This drill illustrates a random experiment with distribution. To help Piel decide, below is the partial table for the means and standard deviations of the random variable, Y, or the number of times he shoot the ball in a shooting spot. Shooting Spot E[Y] SD[Y] Spot 1 0.2 0.4359 Spot 2 0.6 0.7141 Spot 3 0.8 0.8000 Spot 4 the mean of 1.4 by will…