Based on the information above, what is the probability of the astronomer overestimating the distance by 2,330 km or more?

To calculate the probability of the astronomer overestimating the distance by 2,330 km or more, we can follow these steps:

1. ### Break Down the Problem

We need to find the probability $P(X \geq 2330)$, where $X$ is the random variable representing the overestimation in kilometers. The calculation assumes we have a normal distribution (as is common in such problems).

2. ### Relevant Concepts

If $X$ is normally distributed, we will use the following:

• Mean $\mu$
• Standard deviation $\sigma$ The z-score is calculated as: $z = \frac{X - \mu}{\sigma}$

3. ### Analysis and Detail

To proceed, we need the values of $\mu$ and $\sigma$. Assuming we have these values:

• Mean $\mu$: (Enter the mean distance overestimation in km)
• Standard deviation $\sigma$: (Enter the standard deviation of the distance overestimations in km)

Next, we will calculate the z-score for $X = 2330$.

$z = \frac{2330 - \mu}{\sigma}$

Once we find the z-score, we can look up the z-value in the standard normal distribution table or use a calculator to find the corresponding probability $P(Z > z)$.

4. ### Verify and Summarize

Check the z-score calculation and ensure it aligns with the statistical table to find the probability. The final answer will be $P(X \geq 2330) = 1 - P(Z < z)$.

Final Answer

The probability $P(X \geq 2330)$ is calculated based on the provided $\mu$ and $\sigma$. If you provide these values, I can help calculate the exact probability.