Which of the following statements is incorrect?

An inspection procedure at a manufacturing plant involves picking three items at random and then accepting the whole lot if at least two of the three items are in perfect condition. If in reality 91 percent of the whole lot is perfect, what is the probability that the lot will be accepted?

In a recent poll, only 6 percent of the American public say they have significant confidence in Congress. In a random sample of five people, what is the probability that at least one has significant confidence in Congress?

Suppose we have a random variable X where the probability associated with the value k is \(\binom{15}{k}(0.28)^k(0.72)^{15-k}\) for \(k = 0, ..., 15\). What is the mean of X?

It is estimated that 20 percent of all backseat passengers don't wear seat belts. In a random sample of 5 backseat passengers, what is the probability that at least two don't wear seat belts?

You win a game if you toss a fair die with 5 coming up in exactly 1/6 of the tosses. Would you rather flip 12 times or 120 times?

A polygraph test (lie detector) will indicate a lie 5 percent of the time when a person is telling the truth and 98 percent of the time when a person is lying. Suppose three suspects, all innocent and telling the truth, are given polygraph tests. What is the probability that at least one of them is falsely accused of lying?

Suppose we have a binomial random variable where the probability of exactly five successes is \(\binom{n}{5}p^5(0.41)^8\). What is the mean of the distribution?

For which of the following is a binomial an appropriate model?

Suppose the Census Bureau reports a city as having 35 percent African-American residents. If 12 people are randomly selected for a jury, what is the probability that fewer than two of the chosen people are African-American?

A blind taste test is conducted with 6 volunteers. Each is presented with three small cups of water. For each subject, either two of the cups are tap water and the other is bottled water or two of the cups are bottled water and the other is tap water. Each volunteer guesses about which of his/her three cups of water is different from the other two. Suppose 4 volunteers give the correct answer. Could this have happened by chance if they all were blind guessing? What is the probability of at least 4 correct answers if the volunteers were all simply guessing?

Which of the following graphs represents a binomial distribution with \(n = 10\) and \(p = 0.3\)?

A rapid Zika antibody test can be performed in minutes and, if positive, can be followed up by a more time-consuming, more accurate test. Suppose the rapid test results in positive in 2 percent of the population and the more accurate test shows that 94 percent of those who test positive in the rapid test actually have Zika. Assuming that those testing negative in the rapid test do not have Zika, what is the probability that in a random sample of three people, none of them have Zika?

A person has a 7 percent chance of winning the daily office lottery. What is the probability she first wins on the third day?

A manufacturer knows that 15 percent of the widgets coming off the assembly line have a minor defect. If an inspector keeps inspecting units until he comes upon one with the defect, what is the probability he will have to inspect at most four widgets?

It has been estimated that 78.6 percent of all e-mail is spam. On a random day, what is the probability that the first spam e-mail you receive is the fourth e-mail of the day?