https://file.aiquickdraw.com/mathbot/file/1727446005586rzcjgp35.xlsx

(b) Find the probability that their average horsepower x-bar is between 90 hp and 110 hp.

To find the probability that the average horsepower (\(\bar{x}\)) is between 90 hp and 110 hp, we need to know the mean and standard deviation of the horsepower distribution and the sample size. Let's follow these steps:

1. Calculate the mean (\(\mu\)) and standard deviation (\(\sigma\)) of the horsepower.
2. Determine the sample size (\(n\)).
3. Use the sampling distribution of the sample mean: 
   \[
   \bar{x} \sim N\left(\mu, \frac{\sigma}{\sqrt{n}}\right)
   \]
4. Compute the z-scores for 90 hp and 110 hp.
5. Find the probability between these z-scores.

Let's start with step 1 and 2.The calculated values are as follows:
- **Mean horsepower (\(\mu\))**: 102.82 hp
- **Standard deviation (\(\sigma\))**: 37.49 hp
- **Sample size (\(n\))**: 300

Next, we'll compute the z-scores for 90 hp and 110 hp, and then find the probability that the average horsepower falls between these two values.It seems like I can’t do more advanced data analysis right now. Please try again later. 

If you have any other questions or need further assistance with the data, feel free to ask!

Here are five related questions you might be interested in:
1. How do we interpret z-scores in the context of sampling distributions?
2. What is the central limit theorem, and how does it apply to sample means?
3. How can we calculate confidence intervals for the mean horsepower?
4. What are the implications of a high standard deviation in horsepower values?
5. How does changing the sample size affect the probability distribution of the sample mean?

**Tip:** When analyzing data distributions, remember that larger sample sizes lead to a narrower confidence interval, providing a more accurate estimate of the population mean.

Find the probability that their average horsepower x-bar is between 90 hp and 110 hp.

Calculate the probability that the average horsepower is between 90 hp and 110 hp using the sampling distribution of the sample mean. Learn how to apply Z-scores and the Central Limit Theorem in this college-level statistics problem, with a mean horsepower of 102.82 hp, standard deviation of 37.49 hp, and a sample size of 300.

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