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Assignment #4 - CE 311S Due Tuesday 10/2/2012, before 11: Chapter 3 Exercises: 10, 17, 24, 29, 32, 42, 50, 51 And the following 3 problems (worth 12...

If 165 tickets are sold, what is the expected number of passengers who show up for the flight? And for 164 sold tickets?
Q3 part c on document
Assignment #4 – CE 311S Due Tuesday 10/2/2012, before 11:00am , the beginning of class (as always) 100 points + 10 extra credit For this assignment, please solve the following textbook exercises (worth 8 points each): Chapter 3 Exercises: 10, 17, 24, 29, 32, 42, 50, 51 And the following 3 problems (worth 12 points each) Question 1. A chemical supply company currently has in stock 100lb of a certain chemical, which it sells to customers in 5-lb lots. Let X = the number of lots ordered by a randomly chosen customer, and suppose that X has pmf x 1 2 3 4 P ( x ) .20 .3 .2 .20 Compute E ( X) and V ( X ). Then compute the expected number of pounds left after the next customer’s order is shipped, and the variance of the number of pounds left. ( Hint: The number of pounds left is a linear function of X .) Question 2. AirAsia is the largest discount airline operation in the world. The major portion of AirAsia’s fleet consists of Airbus A320-200 aircraft which accommodate 162 passengers each. Due to a marketing policy, AirAsia will overbook flights and issue up to 165 tickets per flight. Define the random variable T as the number of ticketed passengers who actually show up for the flight. The pmf of T appears in the accompanying table. t 155 156 157 158 159 160 161 162 163 164 165 p ( t ) .05 .10 .12 .14 .25 .17 .06 .05 .03 .02 .01 (a) What is the probability that the flight will accommodate all ticketed passengers who show up? (b) What is the probability that not all ticketed passengers who show up can be accommodated? (c) If you are the first person on the standby list (which means you will be the first one to get on the plane, if there are any seats available after all ticketed passengers have been accommodated), what is the probability that you will have a seat on the flight? What is this probability if you are the 4 th person on the standby list? Question 3. Based on a new assessment, Air Asia has determined that 3% of all passengers who purchase tickets do not show up for the flight. Answer the following questions, assuming independence. (a) If 165 tickets are sold, what is the probability that at least one passenger with a ticket cannot be accommodated on the flight? (b) Answer part (a) if 164 tickets are sold. (c) If 165 tickets are sold, what is the expected number of passengers who show up for the flight? And for 164 sold tickets? ( Note: When C(n,m) has large values of n & m, you may need to cancel like terms in the numerator and denominator to get your calculator to solve it without overloading the memory.)

Question 3. Based on a new assessment, Air Asia has determined that 3% of all passengers who
purchase tickets do not show up for the flight. Answer the following questions, assuming
independence....

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