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This problem involves analyzing a normal distribution based on a graph and the text description provided.

### Problem Summary:
The graph represents a normal distribution with mean \( \mu \) and standard deviation \( \sigma \). At a checkpoint on a highway to Åbo, car speeds were measured and found to roughly follow a normal distribution. The data revealed:
- 50% of cars were driving faster than 110 km/h.
- Of these, 32% were driving faster than 120 km/h.

### Solution Approach:
1. **Determine the Mean (\( \mu \)):**
   - From the information that 50% of the cars are driving over 110 km/h, we can deduce that \( 110 \text{ km/h} \) is the mean \( \mu \) of the distribution. This is because, in a normal distribution, the median and the mean are the same, and the point where 50% of the data lies is at the mean.

   Therefore, \( \mu = 110 \text{ km/h} \).

2. **Determine the Standard Deviation (\( \sigma \)):**
   - The text states that 32% of the cars are driving over 120 km/h. From the properties of the normal distribution, the percentage of values falling within certain standard deviations from the mean is known (as shown in the graph):
     - 2% fall beyond \( \mu + 2\sigma \).
     - 14% fall between \( \mu + \sigma \) and \( \mu + 2\sigma \).

   The fact that 32% of cars drive faster than 120 km/h suggests this corresponds to a point between \( \mu + 1\sigma \) and \( \mu + 2\sigma \). So, 120 km/h corresponds roughly to \( \mu + 1\sigma \).

   Using the equation:
   \[
   120 = \mu + \sigma
   \]
   Substituting \( \mu = 110 \text{ km/h} \), we can solve for \( \sigma \):
   \[
   120 = 110 + \sigma
   \]
   \[
   \sigma = 120 - 110 = 10 \text{ km/h}
   \]

### Conclusion:
- The **mean speed** \( \mu \) is **110 km/h**.
- The **standard deviation** \( \sigma \) is **10 km/h**.

Would you like further details or clarifications?

### Related Questions:
1. What is the probability of a car driving slower than 100 km/h based on this distribution?
2. How would the graph change if the standard deviation increased?
3. What percentage of cars drive between 110 km/h and 120 km/h?
4. How can we calculate the probability of a car driving faster than 130 km/h?
5. If we have another checkpoint with a different mean, how do we compare the distributions?

### Tip:
In a normal distribution, approximately 68% of values lie within one standard deviation from the mean, 95% within two, and 99.7% within three.

Grafen beskriver en normalfördelning med medeltalet μ och standardavvikelsen σ. På ett mätställe vid motorvägen till Åbo mättes bilarnas hastighet och man fann att de ungefär följde en normalfördel. Man fann att 50% körde över 110 km/h och av dessa 32% t.o.m. över 120 km/h. Vad är medeltalet och standardavvikelsen?

This example demonstrates how to calculate the mean and standard deviation of a normal distribution from given percentages. In this case, 50% of the data is above 110 km/h, and 32% is above 120 km/h, revealing a mean of 110 km/h and a standard deviation of 10 km/h.

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