HWK4 - MATH 230/STAT 230 Homework 4 Due on 09/29 in class...

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MATH 230/STAT 230: Homework 4 Due on 09/29, in class Read Chapter 2 (excluding Section 2.3), Appendix 1, and Section 3.1 (up to page 148) Problem 1. Let S be the number of successes in 25 independent trials with probability 1 10 of success on each trial. Let m be the most likely value of S. (i) Find m . (ii) Find the probability that P ( S = m ). (iii) What is the normal approximation to P ( S = m ) ? (iv) What is the Poisson approximation to P ( S = m ) ? (v) Repeat (i)-(iv) with the number of trial equal to 250 rather than 25, and success probabil- ity 1 5 , instead of 1 10 . Would the Normal or Poisson approximation give a better approximation in this case ? Problem 2. An airline knows that over the long run, 90% of passengers who reserve seats for a flight show up. On a particular flight with 300 seats, the airline sold 324 reservations. (i) Assuming that passengers show up independently of each other, what is the chance that the flight will be overbooked ? (ii) Suppose that people tend to travel in pairs. What is the chance that the flight will be overbooked ?

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