Question

suppose that the random variable $x$, shown below, represents the number of speeding tickets a person received in a three - year period. $p(x)$ represents the probability of a randomly selected person having received that number of speeding tickets during that period. use the probability distribution table shown below to answer the following questions.

$x$	$p(x)$
1	0.2955
2	0.1521
3	0.0885
4	0.0289
5	0.026
6+	0.0000

a) what is the probability that a randomly selected person has received four tickets in a three - year period? $p(x = 4)=$
b) what is the probability that a randomly selected person has received four or more tickets in a three - year period? $p(xgeq4)=$
c) what is the probability that a randomly selected person has received more than four tickets in a three - year period? $p(x > 4)=$

Explanation:

Step1: Find probability for $x = 4$

From the table, when $x = 4$, $P(x=4)=0.0289$

Step2: Find probability for $x\geq4$

$P(x\geq4)=P(x = 4)+P(x = 5)+P(x=6+)$
$P(x\geq4)=0.0289 + 0.026+0.0000=0.0549$

Step3: Find probability for $x>4$

$P(x>4)=P(x = 5)+P(x=6+)$
$P(x>4)=0.026 + 0.0000=0.026$

Answer:

a) $0.0289$
b) $0.0549$
c) $0.026$