1) A truth serum given to a suspect is known to be 90 percent reliable when the person is guilty and 99 percent reliable when the person is innocent. In other words, 10 percent of the guilty are judged innocent by the serum and 1 percent of the innocent are judged guilty. If the suspect was selected from a group of suspects of which only 5 percent are guilty of having committed a crime, and the serum indicates that the suspect is guilty of having committed a crime, what is the probability that the suspect is innocent?
2) An industry representative claims that 50 percent of all satellite dish owners subscribe to at least one premium movie channel. In an attempt to justify this claim, the representative will poll a randomly selected sample of dish owners. Suppose that the representative's claim is true, and suppose that a sample of four dish owners is randomly selected. Assuming independence, use an appropriate formula to compute
a) The probability that none of the dish owners in the sample subscribes to at least one premium movie channel.
b) The probability that more than two dish owners in the sample subscribe to at least one premium movie channel.
3) A telephone company's goal is to have no more than five monthly line failures on any 100 kilometres of line. The company currently experiences an average of two monthly line failures per 50 kilometres of line. Let x denote the number of monthly line failures per 100 kilometres of line. Assuming x has a Poisson distribution:
a) Find the probability that the company will meet its goal on a particular 100 kilometres of line.
b) Find the probability that the company will not meet its goal on a particular 100 kilometres of line.
4) Among 12 metal parts produced in a machine shop, 3 are defective. If a random sample of three of these metal parts is selected, find
The probability that this sample will contain at least two defectives.
The probability that this sample will contain at most one defective.
5) Weekly demand at a grocery store for a brand of breakfast cereal is normally distributed with a mean of 800 boxes and a standard deviation of 75 boxes. What is the probability that weekly demand is
959 boxes or less?
More than 1,004 boxes?
Less than 650 boxes or greater than 950 boxes?