Question: In the situation of problem 15-8, another sample of 20 flights reveals that 18 of them are full. Obtain the second posterior distribution of the proportion of full flights. Graph the prior distribution of problem 15-8, as well as the first posterior and the second posterior distributions. How did the distribution of the proportion in question change as more information became available?

Problem: American Airlines is interested in the proportion of flights that are full during the 2008 summer season. The airline uses data from past experience and constructs the following prior distribution of the proportion of flights that are full to capacity :

S               P(S)

0.70           0.1

0.75           0.2

0.80           0.3

0.85           0.2

0.90           0.1

0.95           0.1
                 1.0

A sample of 20 flights shows that 17 of these flights are full. Update the probability distribution to obtain a posterior distribution for the proportion of full flights.