Question 6

1. (5 points) Calculate P(X

I. (5 points) Calculate P(X < 3) 2 (5 points) Determine the 80th percentile of X 3. (5 points) Suppose the numbers , , ... , are independently sampled from this distribution. What is the probability that the sum of these numbers is positive? Problem 6 (20 points). In Hilbert's Hotel. there are infinitely many hotel floors, and each floor contains one guest. The guests are randomly ordered throughout the hotel floors. Starting from the first floor going up, you record each guest's height. After a superheroic effort, you pass out from exhaustion after 961 floors. 1. (4 points) What is the population size N? 2- (4 points) What is the sample size n ? 3. (4 points) What percent of the population have you sampled? 40 (8 points) Is the sample mean close to the true population mean ? Justify your answer.