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)
0	0.3034
1	0.2626
2	0.2211
3	0.1458
4	0.0477
5	0.0194
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(x≥4)=

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

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Explanation:

Step1: Find probability for $x = 4$

From the table, when $x = 4$, $P(x=4)=0.0477$.

Step2: Find probability for $x\geq4$

$P(x\geq4)=P(x = 4)+P(x = 5)+P(x\geq6)$. Since $P(x\geq6)=0.0000$, then $P(x\geq4)=0.0477 + 0.0194+0.0000=0.0671$.

Step3: Find probability for $x>4$

$P(x > 4)=P(x = 5)+P(x\geq6)$. Since $P(x\geq6)=0.0000$, then $P(x > 4)=0.0194+0.0000 = 0.0194$.

Answer:

a) $0.0477$
b) $0.0671$
c) $0.0194$