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Penalty Kicks. In the game of soccer, a penalty kick is a direct free kick, taken from 12 yards out from the goal on the penalty mark. According to the article "Penalty Kicks in Soccer: An Empirical Analysis of Shooting Strategies and Goalkeeper's Preferences" (Soccer & Society, Vol. 10, No. 2. pp. 183-191) by M. Bar-Eli and O. Azar, 85% of penalty kicks placed by professional soccer players are successful. In 15 penalty kicks by professional soccer players, what is the probability that

(a) all are successful?

(b) at least 13 are successful?

(c) Find and interpret the mean and standard deviation of the number of successful penalty kicks out of 15.

Pets. According to JAVMA News, a publication of the American Veterinary Medical Association, roughly 60% of U.S. households own one or more pets. Four U.S. households are selected at random. Use Table VII in Appendix A to solve the following problems.

(a) Find the probability that, of the four households sampled, the number that own one or more pets is exactly three; at least three; at most three.

(b) Find the probability distribution of the random variable X. the number of U.S. households in a random sample of four that own one or more pets.

(c) Without referring to the probability distribution obtained in part (b) or constructing a probability histogram, decide whether the probability distribution is right-skewed, symmetric, or left-skewed. Explain your answer. *

Roughly speaking, What is an experiment? an event?

Fill in the blanks.

a.A relative-frequency distribution is to a variable as a ___ distribution is to a random variable.

b. A relative-frequency histogram is to a variable as a ___ histogram is to a random variable.

A variable y of a finite population has the following frequency distribution:

Suppose a member is selected at random from the population and let Y denote the value of the variable y for the member obtained.

a. Determine the probability distribution of the random variable Y.

b. Use random-variable notation to describe the events that Y takes on the value 3, a value less than 3, and a value of at least 3.

c. Find P(Y = 3), P(Y <3), and P(Y 鈮� 3). Interpret your results.

d. Construct a probability histogram for the random variable Y.

A variable y of a finite population has the following frequency distribution:

Suppose a member is selected at random from the population and let Y denote the value of the variable y for the member obtained.

a. Determine the probability distribution of the random variable Y.

b. Use random-variable notation to describe the events that Y takes on the value 3, a value less than 3, and a value of at least 3.

c. Find P(Y = 3), P(Y < 3), and P(Y 3). Interpret your results.

d. Construct a probability histogram for the random variable Y.

Space Shuttles. The National Aeronautics and Space Administration (NASA) compiles data on space-shuttle launches and publishes them on its website. The following table displays a frequency distribution for the number of crew members on each shuttle mission from April 12, 1981 to July 8, 2011.

Let X denote the crew size of a randomly selected shuttle mission between the aforementioned dates.

a. What are the possible values of the random variable X?

b. Use random-variable notation to represent the event that the shuttle mission obtained has a crew size of 7.

c. Find P(X = 4); interpret in terms of percentages.

d. Obtain the probability distribution of X.

e. Construct a probability histogram for X.

Persons per Housing Unit. From the document American Housing Survey for the United States, published by the U.S. Census Bureau, we obtained the following frequency distribution for the number of persons per occupied housing unit, where we have used "7" in place of 鈥�7 or more.鈥� Frequencies are in millions of housing units.

For a randomly selected housing unit, let Y denote the number of persons living in that unit.

a. Identify the possible values of the random variable Y.

b. Use random-variable notation to represent the event that a housing unit has exactly three persons living in it.

c. Determine P(Y = 3); interpret in terms of percentages.

d. Determine the probability distribution of Y.

e. Construct a probability histogram for Y.

Major Hurricanes. The Atlantic Hurricane Database extends back to 1851, recording among other things the number of major hurricanes striking the U.S. Atlantic and Gulf Coast per year. A major hurricane is a hurricane measuring at least a Category 3 on the Saffir-Simpson hurricane wind scale (i.e., with winds of at least 110 mph). As published by the National Oceanic & Atmospheric Administration and the Atlantic Oceanographic & Meteorological Laboratory, the following table provides a probability distribution for the number of major hurricanes, Y, for a randomly selected year between 1851 and 2012.

Use random-variable notation to represent each of the following events. The year had

a. at least one major hurricane.

b. exactly three major hurricanes.

c. between 2 and 4 major hurricanes, inclusive.

Use the special addition rule and the probability distribution to determine

d. P(Y 鈮� 1).

e. P(Y = 3).

f. P(2 鈮� Y鈮� 4)

Dice. When two balanced dice are rolled, 36 equally likely outcomes are possible, as depicted in Fig. 5.1 on page 198. Let Ydenote the sum of the dice.

(a) What are the possible values of the random variable Y?

(b) Use random-variable notation to represent the event that the sum of the dice is 7.

(c) Find $P(Y=7)$.

(d) Find the probability distribution of Y. Leave your probabilities in fraction form.

e. Construct a probability histogram for Y.

In the game of craps, a first roll of a sum of 7 or 11 wins, whereas a first roll of a sum of 2, 3, or 12 loses. To win with any other first sum, that sum must be repeated before a sum of 7 is rolled. Determine the probability of

(f) a win on the first roll.

(g) a loss on the first roll.