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According to an August 2011 survey by the Pew Internet & American Life Project, nearly 40% of adult cell phone owners have downloaded an application ("app") to their cell phone. The accompanying table gives the probability distribution for x, the number of apps used at least once a week by cell phone owners who have downloaded an app to their phone. (The probabilities in the table are based on information from the Pew Internet & American Life Project survey.)

Number of Apps Used, xp(x)0.171.102.113.114.105.106.077.058.039.0210.0211.0212.0213.0214.0115.0116.0117.0118.0119.00520.005\begin{matrix} \text{Number of Apps Used, x} & \text{p(x)}\\ \text{0} & \text{.17}\\ \text{1} & \text{.10}\\ \text{2} & \text{.11}\\ \text{3} & \text{.11}\\ \text{4} & \text{.10}\\ \text{5} & \text{.10}\\ \text{6} & \text{.07}\\ \text{7} & \text{.05}\\ \text{8} & \text{.03}\\ \text{9} & \text{.02}\\ \text{10} & \text{.02}\\ \text{11} & \text{.02}\\ \text{12} & \text{.02}\\ \text{13} & \text{.02}\\ \text{14} & \text{.01}\\ \text{15} & \text{.01}\\ \text{16} & \text{.01}\\ \text{17} & \text{.01}\\ \text{18} & \text{.01}\\ \text{19} & \text{.005}\\ \text{20} & \text{.005}\\ \end{matrix}

a. Show that the properties of a probability distribution for a discrete random variable are satisfied. b. Find P(x10)P(x \geq 10).

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Given:

xp(x)00.1710.1020.1130.1140.1050.1060.0770.0580.0390.02100.02110.02120.02130.02140.01150.01160.01170.01180.01190.005200.005\begin{array}{ c | c } x & p(x) \\ \hline 0 & 0.17 \\ 1 & 0.10 \\ 2 & 0.11 \\ 3 & 0.11 \\ 4 & 0.10 \\ 5 & 0.10 \\ 6 & 0.07 \\ 7 & 0.05 \\ 8 & 0.03 \\ 9 & 0.02 \\ 10 & 0.02 \\ 11 & 0.02 \\ 12 & 0.02 \\ 13 & 0.02 \\ 14 & 0.01 \\ 15 & 0.01 \\ 16 & 0.01 \\ 17 & 0.01 \\ 18 & 0.01 \\ 19 & 0.005 \\ 20 & 0.005 \end{array}

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