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.