1.(5 points) You are the statistician for an airline which still engages in the practice of "overbooking". There are 350 seats on a particular flight. From past data, you know that on average, only 97% of people who pay in advance for a ticket actually show up. (They are sick, get caught in traffic, are delayed by weather, sudden change of plans, or just by a ticket because they don't know their schedule, etc.)

What is the number of tickets (N) that you should sell so that you have only between a 1% and 2 % chance of going over the 350 seat limit?

The binomial equation is 1 = (p + q)^N.

Let the probability of a person buying a ticket actually showing up be p, and q be the probability of the person not showing up.

a.What is the value of p?

b.What is the value of q?

Using the binomial calculator, select the button "above" and put in 350.

c.The value of N is the number of tickets you sell. What is the probability that more than ("above") 350 people will show up if you sell only N = 350 tickets? (Make a "reasonable" guess.)

d.Using the binomial calculator, do you get the same answer that you guessed in (d)? (N = 350, Above 350) (yes or no)

e.Using the binomial calculator, gradually increase the value of N until the probability of getting more than 350 people showing up is between 1% and 2%, meaning .01

2. (5 points) You are the statistician for an airline which still engages in the practice of "overbooking". There are 350 seats on a particular flight. From past data, you know that on average, only 97% of people who pay in advance for a ticket actually show up. (They are sick, get caught in traffic, are delayed by weather, sudden change of plans, or just by a ticket because they don't know their schedule, etc.) What is the number of tickets (N) that you should sell so that you have only between a 1% and 2 % chance of going over the 350 seat limit? The binomial equation is 1 = (p + q). Let the probability of a person buying a ticket actually showing up be p, and q be the probability of the person not showing up. a. What is the value of p? b. What is the value of q? Using the binomial calculator, select the button "above" and put in 350. c. The value of N is the number of tickets you sell. What is the probability that more than ("above") 350 people will show up if you sell only N = 350 tickets? (Make a "reasonable" guess.) d. Using the binomial calculator, do you get the same answer that you guessed in (d)? (N = 350, Above 350) (yes or no) c. Using the binomial calculator, gradually increase the value of N until the probability of getting more than 350 people showing up is between 1% and 2%, meaning .01