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Chapter 5: Q1 (page 220)
Is a probability distribution defined if the only possible values of a random variable are 0, 1,2, 3, and P(0) = P(1) = P(2) = P(3) = 1/3?
No, the probability distribution is not defined if the only possible values of a random variable are 0, 1,2, 3, and .
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Notation of 0+ Using the same survey from Exercise 3, the probability of randomly selecting 30 of the 1009 consumers and getting exactly 24 who are comfortable with the drones is represented as 0+. What does 0+ indicate? Does 0+ indicate that it is impossible to get exactly 24 consumers who are comfortable with the drones?
Geometric Distribution If a procedure meets all the conditions of a binomial distribution except that the number of trials is not fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given by , where p is the probability of success on any one trial. Subjects are randomly selected for the National Health and Nutrition Examination Survey conducted by the National Center for Health Statistics, Centers for Disease Control and Prevention. The probability that someone is a universal donor (with group O and type Rh negative blood) is 0.06. Find the probability that the first subject to be a universal blood donor is the fifth person selected.
In Exercises 6鈥�10, use the following: Five American Airlines flights are randomly selected, and the table in the margin lists the probabilities for the number that arrive on time (based on data from the Department of Transportation). Assume that five flights are randomly selected.
What does the probability of 0+ indicate? Does it indicate that among five randomly selectedflights, it is impossible for none of them to arrive on time?
x | P(x) |
0 | 0+ |
1 | 0.006 |
2 | 0.051 |
3 | 0.205 |
4 | 0.409 |
5 | 0.328 |
In Exercises 21鈥�25, refer to the accompanyingtable, which describes the numbers of adults in groups of five who reported sleepwalking (based on data from 鈥淧revalence and Comorbidity of Nocturnal Wandering In the U.S. Adult General Population,鈥� by Ohayon et al., Neurology, Vol. 78, No. 20).
Use the range rule of thumb to determine whether 4 is a significantly high number of sleepwalkersin a group of 5 adults.
x | P(x) |
0 | 0.172 |
1 | 0.363 |
2 | 0.306 |
3 | 0.129 |
4 | 0.027 |
5 | 0.002 |
In Exercises 15鈥�20, assume that random guesses are made for eight multiple choice questions on an SAT test, so that there are n = 8 trials, each with probability of success (correct) given by p = 0.20. Find the indicated probability for the number of correct answers.
Find the probability that the number x of correct answers is exactly 7.
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