Answer
The distribution obeys the Rules for a Discrete Probability Distribution (see page 323)
Work Step by Step
1) $ΣP(x)=P(0)+P(1)+P(2)+P(3)+P(4)+P(5)=0.1677+0.3354+0.2857+0.1491+0.0373+0.0248=1$
2) $0\leq P(0)\leq1$
$0\leq P(1)\leq1$
$0\leq P(2)\leq1$
$0\leq P(3)\leq1$
$0\leq P(4)\leq1$
$0\leq P(5)\leq1$