In a press release dated October 2, 2008, The National Cyber Security Alliance reported that approximately 80% of adult Americans who own a computer claim to have a firewall installed on their computer to prevent hackers from stealing personal information. This estimate was based on a survey of 3,000 people. It was also reported that in a study of 400 computers, only about 40% actually had a firewall installed.
a. Suppose that the true proportion of computer owners who have a firewall installed is 0.80. If 20 computer owners are selected at random, what is the probability that more than 15 have a firewall installed?
b. Suppose that the true proportion of computer owners who have a firewall installed is 0.40. If 20 computer owners are selected at random, what is the probability that more than 15 have a firewall installed?
c. Suppose that a random sample of 20 computer owners is selected and that 14 have a firewall installed. Is it more likely that the true proportion of computer owners who have a firewall installed is 0.40 or 0.80? Justify your answer based on probability calculations.