Suppose S1 and S2 are open sets in the complex plane a)Discuss:Is the union S1US2 an open set? If you think the statement is true try to prove it.If you think the statement is false,find a counterexample. b)Repeat part a for the intersection of S1 and S2. Solution A set A is an open set if and only if for every point x in A, there is a neighborhood Q of x such that Q is a subset A. Let the two open sets be S1 and S2, and their union is T. Let x be any point x in T. If x is in S1, then let Q be the neighborhood Q subset S1, otherwise let Q be the neighborhood of x in S2. Eitherway, Q is a subset T. Therefore, for every x, there is a neighborhood Q of x that is a subset of T. Hence, T, the union of two open sets, is open. b) Let U = S1S2 Consider any element x in U. Then x is in S1 as well as S2. As both S1 and S2 are open there exists a neighbourhood Q consisting of infinite points of S1 and S2. Or in other words U is open. Hence Intersection of two open sets is always open..

1. Suppose SAT scores are normally distributed with mean 500 and standard deviation 100.
1). What is the probability that a student's SAT score exceeds 650?
2). Above what SAT score value are the upper 40% of students' SAT scores?
3). If four students are randomly selected, what is the probability that their total SAT score
exceeds 2200?
4). SAT scores of 10 students are considered, let Y represent total number of students with SAT
score higher than 650. What is P(Y>= 1)?
Solution
Given that
mean mu = 500
Population standard deviation sigma= 100
Let Z =(X