7. Mensa is an organization that allows people to join only if their Stanford-Binet IQs are in the top 2% of the pop- ulation. Assume the population mean of Stanford-Binet IQs is 100, and the standard deviation is 15, and that the population is normally distributed. (a) What is the lowest Stanford-Binet IQ you could have and still be eligible to join Mensa? (b) What is 99th percentile for the Stanford-Binet IQ scores? (c) What is the probability that a randomly selected per- sons Stanford-Binet IQ is between 85 and 115? (d) What is the probability that two randomly selected people both have Stanford-Binet IQs which qualify them for Mensa? 8. Assume that a multiple choice quiz has 10 questions, each with five choices. Assume a student must select only one answer for each of the 10 questions. Assume further each question is independent, that every choice is equally likely to be selected, and that there is one correct answer. (a) What are the values of n and p? (b) Find the probability that a student answers all ques- tions correctly. (c) Find the probability that a student gets at least 2 questions correct. (d) What grade should the professor expect the class to get on average for this quiz?3. You must use properties of linear combinations of random variables to solve these problems. (a) Let X be a random variable where ux = 3, 0x = 9. Find the mean and the variance of Y, where Y = -2+4X (b) Let X be a random variable where (x = 0, of 1/4. Find the mean and the variance of Y, where Y = -10- 3X 4. Answer the questions with TRUE or FALSE and explain your answers as well. (a) If we have 5 binomial trials, and Y =# of successes in the 5 trials, Y can take on only values {1, 2, 3, 4,5}. (b) If a random variable Y only takes on values {0, 0.1, 0.2, 0.3, 0.4}, it is a discrete random variable. (c) The probability of the intersection of two events could be higher than the probability of the union of two events