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Chapter 5: Q 5.6. (page 200)
An experiment has 40 possible outcomes, all equally likely. An event can occur in 25 ways. The probability that the event is .
The probability that the event is.
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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.
Interpret each of the following probability statements, using the frequentist interpretation of probability.
(a). The probability is 0.487 that a newborn baby will be a girl.
(b). The probability of a single ticket winning a prize in the Powerball lottery is 0.031.
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. *
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.
| Person | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Frequencies | 27.9 | 34.4 | 17.0 | 15.5 | 6.8 | 2.3 | 1.4 |
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.
Expressing Confidence Intervals Example 2 showed how the statistics of n= 22 ands= 14.3 result in this 95% confidence interval estimate of \(\sigma \): 11.0 < \(\sigma \) < 20.4. That confidence interval can also be expressed as (11.0, 20.4), but it cannot be expressed as 15.7 \( \pm \) 4.7. Given that 15.7\( \pm \)4.7 results in values of 11.0 and 20.4, why is it wrong to express the confidence interval as 15.7\( \pm \)4.7?
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