Suppose that the random variable xx, shown below, represents the number of speeding tickets a person received in a three-year period. P(x)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. xx P(x)P(x) 0 0.287 1 0.2846 2 0.2375 3 0.0992 4 0.0471 5 0.0446 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)=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)=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)=P(x>4)= d) Would it be unusual to randomly select a person who has received four tickets in a three-year period? Yes No e) Which probability should we use to determine whether or not it is unusual to randomly select a person who has received four tickets in a three-year period? P(x=4)P(x=4) P(x>4)P(x>4) P(x≥4)
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Suppose that the random variable xx, shown below, represents the number of speeding tickets a person received in a three-year period. P(x)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.
| xx | P(x)P(x) |
|---|---|
| 0 | 0.287 |
| 1 | 0.2846 |
| 2 | 0.2375 |
| 3 | 0.0992 |
| 4 | 0.0471 |
| 5 | 0.0446 |
| 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)=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)=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)=P(x>4)=
d) Would it be unusual to randomly select a person who has received four tickets in a three-year period?
- Yes
- No
e) Which probability should we use to determine whether or not it is unusual to randomly select a person who has received four tickets in a three-year period?
- P(x=4)P(x=4)
- P(x>4)P(x>4)
- P(x≥4)
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