FDIC bank failures. The Federal Deposit Insurance Corporation (FDIC) normally insures deposits of up to $\$ 100,000$ in banks that are members of the Federal Reserve System against losses due to bank failure or theft. Over the last 10 years, the average number of bank failures per year among insured banks was 52 (FDIC Failed Bank List, 2016). Assume that $x$, the number of bank failures per year among insured banks, can be adequately characterized by a Poisson probability distribution with mean 52 . Find the expected value and standard deviation of $x$.

Working on summer vacation. Recall (Exercise 3.13, p. 145) that a Harris Interactive (July 2013) poll found that $22 \%$ of U.S. adults do not work at all while on summer vacation. In a random sample of 10 U.S. adults, let $x$ represent the number who do not work during summer vacation. Find the probability that 2 or fewer of the 10 U.S. adults do not work during summer vacation.

Working on summer vacation. Refer to the Harris Interactive (July 2013) poll of whether U.S. adults work during summer vacation, Exercise $3.13$ (p. 145). Recall that the poll found that $61 \%$ of the respondents work during their summer vacation, $22 \%$ do not work at all while on vacation, and $17 \%$ were unemployed. Also, $38 \%$ of those who work while on vacation do so by monitoring their business emails. What is the probability that a randomly selected poll respondent will work while on summer vacation and will monitor business emails?

Working on summer vacation. Recall (Exercise 3.13, p. 145) that a Harris Interactive (July 2013) poll found that $22 \%$ of U.S. adults do not work at all while on summer vacation. In a random sample of 10 U.S. adults, let $x$ represent the number who do not work during summer vacation. Give the value of $p$ for this binomial experiment.

Working on summer vacation. Recall (Exercise 3.13, p. 145) that a Harris Interactive (July 2013) poll found that $22 \%$ of U.S. adults do not work at all while on summer vacation. In a random sample of 10 U.S. adults, let $x$ represent the number who do not work during summer vacation. Explain why $x$ is (approximately) a binomial random variable.

Working on summer vacation. Recall (Exercise $3.13$, p. 145) that a Harris Interactive (July 2013) poll found that $22 \%$ of U.S. adults do not work at all while on summer vacation. In a random sample of 10 U.S. adults, let $x$ represent the number who do not work during summer vacation. For this experiment, define the event that represents a "success."

Working on summer vacation. Recall (Exercise 3.13, p. 145) that a Harris Interactive (July 2013) poll found that $22 \%$ of U.S. adults do not work at all while on summer vacation. In a random sample of 10 U.S. adults, let $x$ represent the number who do not work during summer vacation. Find $P(x=3)$.

Physicians' opinions on a career in medicine. The Physicians' Foundation reported that $58 \%$ of all general practice physicians in the United States do not recommend medicine as a career (The Physicians' Foundation 2012 Survey of America's Physicians). Let $x$ represent the number of sampled general practice physicians who do not recommend medicine as a career. Explain why $x$ is approximately a binomial random variable.

Identity theft victims. According to The National Crime Victimization Survey (September 2015), published by the U.S. Department of Justice, about $17.6$ million people were victims of identity theft over the past year. This number represents $7 \%$ of all persons age 16 or older in the United States. Of these victims, $86 \%$ reported that the identity theft occurred from the unauthorized use of a credit card. Consider a randomly selected person of age 16 or older in the United States. What is the probability that this person was a victim of identity theft that occurred from the unauthorized use of a credit card?

Identity theft victims. According to The National Crime Victimization Survey (September 2015), published by the U.S. Department of Justice, about $17.6$ million people were victims of identity theft over the past year. This number represents $7 \%$ of all persons age 16 or older in the United States. Of these victims, $86 \%$ reported that the identity theft occurred from the unauthorized use of a credit card. Consider a randomly selected person of age 16 or older in the United States. What is the probability that this person was a victim of identity theft?

Give two reasons why the crimes statistics reported by the Uniform Crime Reports differ from those statistics reported by the National Crime Victimization Survey. Which report would you consider more reliable and why?

The Journal of the American Law and Economics Association (Vol. 3, 2001) published the results of a study of appeals of federal civil trials. The accompanying table, extracted from the article, gives a breakdown of 2,143 civil cases that were appealed by either the plaintiff or the defendant. The outcome of the appeal, as well as the type of trial (judge or jury), was determined for each civil case. Suppose one of the 2,143 cases is selected at random and both the outcome of the appeal and the type of trial are observed.

$$\begin{matrix} \text{ } & \text{Jury} & \text{Judge} & \text{Totals}\\ \text{Plaintiff trial win-reversed} & \text{194} & \text{71} & \text{265}\\ \text{Plaintiff trial win-affirmed/dismissed} & \text{429} & \text{240} & \text{669}\\ \text{Defendant trial win-reversed} & \text{111} & \text{68} & \text{179}\\ \text{Defendant trial win - affirmed/dismissed} & \text{731} & \text{299} & \text{1,030}\\ \text{Totals} & \text{1,465} & \text{678} & \text{2,143}\\ \end{matrix}$$

Find $P(A \cup B)$.

The Journal of the American Law and Economics Association (Vol. 3, 2001) published the results of a study of appeals of federal civil trials. The accompanying table, extracted from the article, gives a breakdown of 2,143 civil cases that were appealed by either the plaintiff or the defendant. The outcome of the appeal, as well as the type of trial (judge or jury), was determined for each civil case. Suppose one of the 2,143 cases is selected at random and both the outcome of the appeal and the type of trial are observed.

$$\begin{matrix} \text{ } & \text{Jury} & \text{Judge} & \text{Totals}\\ \text{Plaintiff trial win-reversed} & \text{194} & \text{71} & \text{265}\\ \text{Plaintiff trial win-affirmed/dismissed} & \text{429} & \text{240} & \text{669}\\ \text{Defendant trial win-reversed} & \text{111} & \text{68} & \text{179}\\ \text{Defendant trial win - affirmed/dismissed} & \text{731} & \text{299} & \text{1,030}\\ \text{Totals} & \text{1,465} & \text{678} & \text{2,143}\\ \end{matrix}$$

Find $P(A \cap B)$.

The Journal of the American Law and Economics Association (Vol. 3, 2001) published the results of a study of appeals of federal civil trials. The accompanying table, extracted from the article, gives a breakdown of 2,143 civil cases that were appealed by either the plaintiff or the defendant. The outcome of the appeal, as well as the type of trial (judge or jury), was determined for each civil case. Suppose one of the 2,143 cases is selected at random and both the outcome of the appeal and the type of trial are observed.

$$\begin{matrix} \text{ } & \text{Jury} & \text{Judge} & \text{Totals}\\ \text{Plaintiff trial win-reversed} & \text{194} & \text{71} & \text{265}\\ \text{Plaintiff trial win-affirmed/dismissed} & \text{429} & \text{240} & \text{669}\\ \text{Defendant trial win-reversed} & \text{111} & \text{68} & \text{179}\\ \text{Defendant trial win - affirmed/dismissed} & \text{731} & \text{299} & \text{1,030}\\ \text{Totals} & \text{1,465} & \text{678} & \text{2,143}\\ \end{matrix}$$

Find $P\left(A^{c}\right)$