2. Suppose your final grade on a particular standardized test is determined by the formula below: G = 0.4M + 0.1E + 0.3P + 0.2B where G is your overall grade, and M, E, P, and B represent your math, english, physics, and biology scores, respectively. All of these scores are on a 0-100 scale, but suppose that scores above 100 are possible through extra credit on bonus problems. Your score in each category are random variables, which you assume are independent of one another, and you choose their distributions to represent your confidence in how youll perform in each category. Suppose M N(M = 90, M = 5), E N(E = 70, E = 10), P N(P = 90, P = 4), and B N(B = 80, B = 8), where N(, ) denotes a normal distribution with mean and standard deviation .

Suppose you want to improve your english score so that the probability of your overall score being at least 85 is at least 95%. So, E is an unknown quantity that you want to figure out, but all the other parameters for the normal distributions remain the same. What is the minimum mean for the distribution of english scores to give you a 95% probability of earning a 85 or above?