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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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In Exercises 15鈥�20, refer to the accompanying table, which describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children.
Use the range rule of thumb to determine whether 1 girl in 8 births is a significantly low number of girls.
Number of girls x | P(x) |
0 | 0.004 |
1 | 0.031 |
2 | 0.109 |
3 | 0.219 |
4 | 0.273 |
5 | 0.219 |
6 | 0.109 |
7 | 0.031 |
8 | 0.004 |
In Exercises 21鈥�24, assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes (based on data from an LG Smartphone survey).
If 20 adult smartphone users are randomly selected, find the probability that exactly 15 of them use their smartphones in meetings or classes.
In Exercises 21鈥�25, refer to the accompanying table, 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).
Find the mean and standard deviation for the numbers of sleepwalkers in groups of five.
x | P(x) |
0 | 0.172 |
1 | 0.363 |
2 | 0.306 |
3 | 0.129 |
4 | 0.027 |
5 | 0.002 |
In Exercises 21鈥�24, assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes (based on data from an LG Smartphone survey).
If 12 adult smartphone users are randomly selected, find the probability that fewer than 3 of them use their smartphones in meetings or classes.
Drone Deliveries Based on a Pitney Bowes survey, assume that 42% of consumers are comfortable having drones deliver their purchases. Suppose we want to find the probability that when five consumers are randomly selected, exactly two of them are comfortable with the drones. What is wrong with using the multiplication rule to find the probability of getting two consumers comfortable with drones followed by three consumers not comfortable, as in this calculation:
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