1. Suppose that we have a sample of 100 people and the random variable Xi is the Height of the ith person (in centimeters). Knowing that all Xi 's are identically distributed and expected value of Xi is 160 and standard deviation is 25, find 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 expected value of Xi is 20 and standard deviation is 8. Find the probability that the waiting time for 50 people is between 900 & 1100 seconds ((9001100) P ( 900 Y 1100 ) )? (25 points) 4. Suppose that the weight of people in a specific town are normally distributed with the mean of 140 pounds and standard deviation of 20 pounds. Answer the following questions: (25 points) Find the percentage of the people who weight less than 130 pounds. Find the percentage of people who weight more than 160 pounds