1. A 50-question true-false exam is given. Each correct answer is worth 10 points. Consider an unprepared student who randomly guesses on each question. • If 5 points are deducted for each incorrect answer, what is the chance that the student will score at least 200 points? • If 10 points are deducted for each wrong answer, what is the chance that the student will get a negative score on the exam? First, define X, the distribution of X, and the two parameters that define this distribution. (5 pts). Then, for each of the two parts: (i) State the probability equation; (ii) State the Excel formula; (iii) State the numerical answer. (12 pts for (i) and (ii); 3 pts for (iii); total 20 pts) 2. A manager of boiler drums wants to use regression to predict the number of mean worker-hours (Y) needed to erect the drums in future projects. Data for 36 boilers have been collected and is given in Boilers excel worksheet. In the dataset, there are also data corresponding to boiler capacity (pounds); boiler design pressure (psi); boiler type and drum type. (25 pts)