1. Suppose that we have a sample of 100 people and the random variable X1 is the Height of the ith person (in centimeters). Knowing that all X; 's are identically distributed and EX,- 2 ,u = 160 and ox]. = 0' = 25, nd the probability that the total height of these people is smaller than 17,000 cm. (25 points) 2. Assuming that our random variable Y belongs to Binomial distribution and Y~ Binomial (n = 36, p = 1/3). Find the probability that Y > 14. (25 points) 3. The random variable Xi is the waiting time (in seconds} for the elevator to arrive once the ith person push the button and EX,- = y = 20 and ox}. = o- = 8. Find the probability that the waiting time for 50 people is between 900 & 1100 seconds (P (900 g Y s 1100))? (25 points) 4. Suppose that the weight of people in a specic town are normally distributed with the mean of 140 pounds and standard deviation of 20 pounds. Answer the following questions: (25 points) A. Find the percentage of the people who weight less than 130 pounds. B. Find the percentage of people who weight more than 160 pounds