https://file.aiquickdraw.com/mathbot/file/1730290771283r7t1hbik.jpg

To find the mean, standard deviation, maximum, and IQR of all the potential fines based on the given information, let’s break down the problem.

### Given Information:
1. **Mean speed** of speeders = 29 mph
2. **Standard deviation** of speeds = 2.4 mph
3. **Maximum speed** recorded = 34 mph
4. **Interquartile range (IQR)** of speeds = 3.2 mph
5. **Speed limit** = 20 mph
6. **Fine structure**:
   - $60 base fine
   - Additional $10 for each mph over the speed limit

### Step-by-Step Solution:

1. **Convert the Mean Speed to the Mean Fine:**
   - Mean speed of speeders = 29 mph
   - Speed over the limit = 29 - 20 = 9 mph
   - Fine for mean speed: $ 60 + (10 \times 9) = 60 + 90 = 150 $

2. **Convert the Standard Deviation of Speeds to the Standard Deviation of Fines:**
   - Since the fine increases by $10 for each mph over the limit, we multiply the standard deviation in speed by $10.
   - Standard deviation of fines = $ 2.4 \times 10 = 24 $

3. **Convert the Maximum Speed to the Maximum Fine:**
   - Maximum speed = 34 mph
   - Speed over the limit = 34 - 20 = 14 mph
   - Fine for maximum speed: $ 60 + (10 \times 14) = 60 + 140 = 200 $

4. **Convert the IQR of Speeds to the IQR of Fines:**
   - IQR in speed = 3.2 mph
   - Since each mph over the limit corresponds to an additional $10, the IQR in fines = $ 3.2 \times 10 = 32 $

### Summary of Answers:
- **Mean of fines** = $150
- **Standard deviation of fines** = $24
- **Maximum fine** = $200
- **IQR of fines** = $32

Let me know if you would like further clarification on any of these steps.

---

### Related Questions:
1. How would the mean fine change if the speed limit was raised by 5 mph?
2. What would the fine be if a driver was going exactly 35 mph?
3. How would a change in the fine structure (e.g., $15 per mph over the limit) affect the mean fine?
4. Can the fine distribution be considered normal if speeds are normally distributed?
5. What would be the effect on fines if the IQR of speeds increased?

### Tip:
To convert statistics like mean and standard deviation when dealing with a fixed multiplier, multiply the statistics by that constant, as we did here with fines and speeds.

A homeowner recorded the speeds of cars driving past his house, where the speed limit is 20 mph. The mean of 100 readings was 24.24 mph, with a standard deviation of 3.79 mph. (The homeowner actually recorded every car for a two-month period. These are 100 representative readings.) Suppose police set up radar surveillance on the street. For the many speeders who got tickets the mean was 29 mph, with a standard deviation of 2.4 mph, a maximum of 34 mph, and an IQR of 3.2 mph. Local law prescribes fines of $60, plus $10 per mile per hour over the 20 mph speed limit. For example, a driver convicted of going 25 mph would be fined $60 + $10(5) = $110. Find the mean, standard deviation, maximum, and IQR of all the potential fines.

Solve a statistics problem involving speed fines, where a homeowner records car speeds, and police radar surveillance measures the fines for speeders. Learn how to calculate the mean, standard deviation, maximum, and IQR of potential fines with fines based on speed over a limit.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation