Due: December 5, 2012
Show all your works.
It is known that screws produced by a certain company will be defective with probability 0.01 independently of each other. The company sells screws in packages of 10 and offers a money-back guarantee that at most 1 of the 10 screws is defective. What proportion of package sold must the company replace?
A local bank reviewed its credit card policy with the intention of recalling some of its credit cards. In the past approximately 5% of cardholders defaulted, leaving the bank unable to collect the outstanding balance. Hence, management established a prior probability of 0.05 that any particular cardholder will default. The bank also found that the probability of missing a monthly payment is 0.2 for customers who do not default. Of course, the probability of missing a monthly payment for those who default is 1.
Fifty percent of Americans believed the country was in a recession, even though technically the economy had not shown two straight quarters of negative growth. For a sample of 20 Americans, make the following calculations.
Given that a customer missed one of more monthly payments, compute the posterior probability that the customer will default.
The bank would like to recall its card if the probability that a customer will default is greater than 0.2. Should the bank recall its card if the customer misses a monthly payment? Why or why not?
Compute the probability that exactly 12 people believed the country was in a recession. Compute the probability that no more than three people believed the country was in a recession.
How many people would you expect to say the country was in a recession? Compute the variance and standard deviation of the number of people who believed the country was in a recession.
A small plane has gone down, and the search is organized into three regions. likeliest, they are: