4) ### Speeding Ticket Probability Analysis on I-25 in ColoradoThis section provides a statistical analysis of speeding tickets issued on I-25 in Colorado, based on a sample of 54 tickets. #### Dataset TableThe table below displays the distribution of speeding tickets by gender and speeding ranges:| Speed Over Limit | Male | Female | Total ||------------------------|------|--------|-------|| 0-10 mph over limit | 6 | 4 | 10 || 10-20 mph over limit | 18 | 9 | 27 || More than 20 mph over limit | 11 | 6 | 17 || **Total** | 35 | 19 | 54 |#### Questions and Analysis1. **Random Ticket Probability: Female Driver** - Calculate the probability that a randomly selected ticket was issued to a female driver. - Probability $ P(\text{Female}) $ = (Number of tickets issued to females) / (Total number of tickets) - $ P(\text{Female}) = \frac{19}{54} $2. **Conditional Probability: Male Offender Exceeding 20 mph** - Given that a particular ticket was issued to a male driver, compute the likelihood that he was driving more than 20 mph over the limit. - Probability $ P(\text{More than 20 mph over limit} | \text{Male}) $ = $\frac{\text{Number of male tickets for more than 20 mph}}{\text{Total male tickets}}$ - $ P(\text{More than 20 mph over limit} | \text{Male}) = \frac{11}{35} $3. **Conditional Probability: Female Driver Exceeding 10-20 mph** - Given a particular ticket had the driver speeding 10-20 mph over the limit, find out the probability that the driver was female. - Probability $ P(\text{Female} | \text{10-20 mph over limit}) $ = $\frac{\text{Number of female tickets for 10-20 mph}}{\text{Total number of tickets for 10-20 mph}}$ - \( P(\text{Female} | \text{10-20 mph over limit}) = \frac{9}{27}

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Description: 4) ### Speeding Ticket Probability Analysis on I-25 in ColoradoThis section provides a statistical analysis of speeding tickets issued on I-25 in Colorado, based on a sample of 54 tickets. #### Dataset TableThe table below displays the distribution o

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The table below lists a random sample of 54 speeding tickets on l-25 in Colorado. 0-10 mph over limit 10-20 mph over limit More than 20 mph over limit Total Male 6. 18 11 35 Female 4 6. 6. 19 Total 10 27 17 54 (Note: PLease enter your answer as a decimal number rounded to 4 decimals accuracy, NO FRACTIONS) a) If a random ticket was selected, what would be the probability that the driver was female? b) Given that a particular ticket had a male offender, what is the probability that they were more than 20 mph over the limit? c) Given that a particular ticket was 10-20 mph over the limit, what is the probability that the driver was female? LHit that the driver was a male?

The table below lists a random sample of 54 speeding tickets on l-25 in Colorado. 0-10 mph over limit 10-20 mph over limit More than 20 mph over limit Total Male 6. 18 11 35 Female 4 6. 6. 19 Total 10 27 17 54 (Note: PLease enter your answer as a decimal number rounded to 4 decimals accuracy, NO FRACTIONS) a) If a random ticket was selected, what would be the probability that the driver was female? b) Given that a particular ticket had a male offender, what is the probability that they were more than 20 mph over the limit? c) Given that a particular ticket was 10-20 mph over the limit, what is the probability that the driver was female? LHit that the driver was a male?

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Author:Amos Gilat

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Concept explainers

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.

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Question

### Speeding Ticket Probability Analysis on I-25 in Colorado

This section provides a statistical analysis of speeding tickets issued on I-25 in Colorado, based on a sample of 54 tickets.

#### Dataset Table

The table below displays the distribution of speeding tickets by gender and speeding ranges:

| Speed Over Limit | Male | Female | Total |
|------------------------|------|--------|-------|
| 0-10 mph over limit | 6 | 4 | 10 |
| 10-20 mph over limit | 18 | 9 | 27 |
| More than 20 mph over limit | 11 | 6 | 17 |
| **Total** | 35 | 19 | 54 |

#### Questions and Analysis

1. **Random Ticket Probability: Female Driver**
- Calculate the probability that a randomly selected ticket was issued to a female driver.
- Probability $ P(\text{Female}) $ = (Number of tickets issued to females) / (Total number of tickets)
- $ P(\text{Female}) = \frac{19}{54} $

2. **Conditional Probability: Male Offender Exceeding 20 mph**
- Given that a particular ticket was issued to a male driver, compute the likelihood that he was driving more than 20 mph over the limit.
- Probability $ P(\text{More than 20 mph over limit} | \text{Male}) $ = $\frac{\text{Number of male tickets for more than 20 mph}}{\text{Total male tickets}}$
- $ P(\text{More than 20 mph over limit} | \text{Male}) = \frac{11}{35} $

3. **Conditional Probability: Female Driver Exceeding 10-20 mph**
- Given a particular ticket had the driver speeding 10-20 mph over the limit, find out the probability that the driver was female.
- Probability $ P(\text{Female} | \text{10-20 mph over limit}) $ = $\frac{\text{Number of female tickets for 10-20 mph}}{\text{Total number of tickets for 10-20 mph}}$
- \( P(\text{Female} | \text{10-20 mph over limit}) = \frac{9}{27}

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