According to the U.S. Census​ Bureau, the mean of the commute time to work for a resident of New Orleans, Louisiana is 25.8 minutes. Assume that the standard deviation of the commute time is 6.3 minutes to complete parts​ (a) through​ (c).

Let's analyze the problem based on the information provided:

- The **mean** commute time (\(\mu\)) is **25.8 minutes**.
- The **standard deviation** (\(\sigma\)) is **6.3 minutes**.

Now, let's proceed to complete the tasks for parts (a) through (c). These tasks typically involve probabilities or related statistics.

### (a) Probability of a commute time greater than a specific value
We can compute the probability that a randomly selected resident has a commute time greater than a certain value using the **z-score** formula:

\[
z = \frac{x - \mu}{\sigma}
\]

where \(x\) is the specific commute time, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

Please provide the specific value for part (a), or if you prefer, I can guide you on how to calculate it for a general case.

### (b) Probability of a commute time less than a specific value
Similarly, the probability of having a commute time **less than** a specific value can also be calculated using the z-score formula, and then we use the **standard normal distribution** to find the probability.

Again, if you have a specific value, we can proceed with that.

### (c) Commuting time within a certain range
If you want to find the probability that a commute time falls **within a certain range** (e.g., between \(x_1\) and \(x_2\)), we will calculate the z-scores for both \(x_1\) and \(x_2\) and then find the area under the normal distribution curve between them.

Let me know if you would like to calculate these values for specific commute times, or if you need further clarification!

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Would you like further details on how to approach these calculations?  
Here are some related questions for practice:

1. What is the probability that a randomly selected resident has a commute time of more than 30 minutes?
2. How do you calculate the probability of a commute time less than 20 minutes?
3. What is the probability that a resident has a commute time between 15 and 35 minutes?
4. How do we interpret a z-score in the context of commute times?
5. How does the shape of the normal distribution curve change with varying standard deviations?

**Tip**: The z-score gives a quick way to understand how far a particular value is from the mean, measured in units of standard deviation.

Solve a normal distribution problem involving commute times for New Orleans residents, where the mean is 25.8 minutes and the standard deviation is 6.3 minutes. Learn how to calculate probabilities for specific times using z-scores. Suitable for high school statistics students.

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