Review Exercises 225 4 Review Exercises Section 4.1 In Exercises 1 and 2, determine whether the random variable x is discrete or continuous. Explain. 1. Let x represent the grade on an exam worth a total of 100 points. 2. Let x represent the weight of a truck at a weigh station. In Exercises 3 and 4, (a) construct a probability distribution, and (b) graph the probability distribution using a histogram and describe its shape. 3. The number of hits per game played by a Major League Baseball player Hits 0 1 2 3 4 5 Games 2962331231 4. The number of hours students in a college class slept the previous night Hours 4 5 6 7 8 9 10 Students 1 6 132314 4 2 In Exercises 5 and 6, determine whether the distribution is a probability distribution. If it is not a probability distribution, explain why. 5. The random variable x represents the number of tickets a police officer writes out each shift. x 0 1 2 3 4 5 P1x2 0.09 0.23 0.29 0.16 0.21 0.02 6. The random variable x represents the number of classes in which a student is enrolled in a given semester at a university. x 1 2 3 4 5 6 7 8 P1x2 1 80 2 75 1 10 12 25 27 20 1 5 2 25 1 120 In Exercises 7 and 8, (a) find the mean, variance, and standard deviation of the probability distribution, and (b) interpret the results. 7. The number of cell phones per household in a small town Cell phones 0 1 2 3 4 5 6 Probability 0.020 0.140 0.272 0.292 0.168 0.076 0.032 8. A television station sells advertising in 15-, 30-, 60-, 90-, and 120-second blocks. The distribution of sales for one 24-hour day is given. Length (in seconds) 15 30 60 90 120 Probability 0.134 0.786 0.053 0.006 0.021
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