There are 1000 students in the senior class at a certain high school. The high school offers two Advanced Placement math/stat classes to seniors only: AP Calculus and AP Statistics. The roster of the Calculus class shows 95 people; the roster of the Statistics class shows 86 people. There are 43 overachieving seniors on both rosters.
1. What is the probability that a random selected senior is in at least one of the two classes?
2. If the student is in the Statistics class, what is the probabilty the student is also in the Calculus class?
3. A random sample of 225 SAT scores has a mean of 1500. Assume that SAT scores have a population standard deviation of 300. Construct a 95% confidence interval estimate of the mean SAT scores.