4. Probability

Interpreting a Computer Display

In Exercises 9–12, refer to the display obtained by using the paired data consisting of weights (pounds) and highway fuel consumption amounts (mi/gal) of the large cars included in Data Set 35 “Car Data” in Appendix B. Along with the paired weights and fuel consumption amounts, StatCrunch was also given the value of 4000 pounds to be used for predicting highway fuel consumption.

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Predicting Highway Fuel Consumption Using a car weight of x = 4000 (pounds), what is the single value that is the best predicted amount of highway fuel consumption?

Casino Size and Revenue Use the same paired data from the preceding exercise.

b. What is the best predicted amount of revenue for a casino with a size of 200 thousand square feet? Is it likely that the best predicted amount of revenue will be accurate?

Federal Criminal Defendants The following graph depicts results from a study of defendants in federal crime cases (based on data from the Administrative Office of the U.S. Courts).

a. If a defendant is randomly selected what is the probability that this person had their case dismissed before going to trial?

Federal Criminal Defendants The following graph depicts results from a study of defendants in federal crime cases (based on data from the Administrative Office of the U.S. Courts).

d. If three defendants are randomly selected, what is the probability that they all pleaded guilty?

Notation For a polygraph (lie detector) used when a subject is presented with a question, let L= the subject lied and let Y = the polygraph indicated that the subject told a lie. Use your own words to translate the notation P (Y|L) into a verbal statement.

Significant For 100 births, P(exactly 56 girls) and P(56 or more girls) Is 56 girls in 100 births a significantly high number of girls? Which probability is relevant to answering that question?

Lottery. In Exercises 15–20, refer to the accompanying table, which describes probabilities for the California Daily 4 lottery. The player selects four digits with repetition allowed, and the random variable x is the number of digits that match those in the same order that they are drawn (for a “straight” bet).

Using Probabilities for Significant Events

a. Find the probability of getting exactly 2 matches.

Lottery. In Exercises 15–20, refer to the accompanying table, which describes probabilities for the California Daily 4 lottery. The player selects four digits with repetition allowed, and the random variable x is the number of digits that match those in the same order that they are drawn (for a “straight” bet).

Using Probabilities for Significant Events

b. Find the probability of getting 2 or more matches.

Lottery. In Exercises 15–20, refer to the accompanying table, which describes probabilities for the California Daily 4 lottery. The player selects four digits with repetition allowed, and the random variable x is the number of digits that match those in the same order that they are drawn (for a “straight” bet).

Using Probabilities for Significant Events

a. Find the probability of getting exactly 3 matches.

Using Probabilities for Significant Events

c. Which probability is relevant for determining whether 3 is a significantly high number of matches: the result from part (a) or part (b)?

Using Probabilities for Significant Events

a. Find the probability of getting exactly 1 match.

Using Probabilities for Significant Events

b. Find the probability of getting 1 or fewer matches.

Using Probabilities for Significant Events

c. Which probability is relevant for determining whether 1 is a significantly low number of matches: the result from part (a) or part (b)?

Using Probabilities for Significant Events

d. Is 1 a significantly low number of matches? Why or why not?

Lottery. In Exercises 15–20, refer to the accompanying table, which describes probabilities for the California Daily 4 lottery. The player selects four digits with repetition allowed, and the random variable x is the number of digits that match those in the same order that they are drawn (for a “straight” bet).

Using Probabilities for Significant Events

b. Find the probability of getting 3 or more matches.