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The question compares the probability of getting an offer of $34,000 or more from two companies:

- **Company A**: Mean salary $ \mu = 28,000 $, standard deviation $ \sigma = 3,000 $.
- **Company B**: Mean salary $ \mu = 28,000 $, standard deviation $ \sigma = 7,000 $.

We need to determine which company is more likely to offer a salary of $34,000 or more.

### Step 1: Calculate Z-scores for each company
The Z-score formula is:
\[
Z = \frac{X - \mu}{\sigma}
\]
where $ X = 34,000 $, $ \mu = 28,000 $, and $ \sigma $ is the standard deviation.

- **For Company A**:
  \[
  Z_A = \frac{34,000 - 28,000}{3,000} = \frac{6,000}{3,000} = 2
  \]
  
- **For Company B**:
  \[
  Z_B = \frac{34,000 - 28,000}{7,000} = \frac{6,000}{7,000} \approx 0.857
  \]

### Step 2: Interpret the Z-scores
- **Company A's Z-score** is 2, meaning the salary of $34,000 is 2 standard deviations above the mean.
- **Company B's Z-score** is approximately 0.857, meaning the salary of $34,000 is less than 1 standard deviation above the mean.

### Step 3: Likelihood based on Z-scores
- A Z-score of **2** corresponds to a smaller probability of getting $34,000 or more (because it's farther from the mean).
- A Z-score of **0.857** corresponds to a higher probability of getting $34,000 or more, as it's closer to the mean.

### Conclusion:
**Company B** is more likely to offer $34,000 or more because it is within a lower number of standard deviations from the mean compared to Company A.

The correct answer is **C: Company B**.

Would you like more details or have any questions?

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Here are 5 related questions you might find interesting:
1. How do you calculate the probability of a specific salary using the Z-score?
2. What is the meaning of the Z-score in terms of normal distribution?
3. How does the standard deviation affect the probability of extreme salary values?
4. Can the Z-score be negative, and if so, what does it mean?
5. How would the probabilities change if the means of the two companies were different?

**Tip**: When comparing probabilities, always check how far the value is from the mean using the Z-score—it gives a quick way to assess likelihood.

You are applying for a job at two companies. Company A offers starting salaries with μ = $28,000 and σ = $3,000. Company B offers starting salaries with μ = $28,000 and σ = $7,000. From which company are you more likely to get an offer of $34,000 or more?

Learn how to compare job offer probabilities from two companies using Z-scores and normal distribution. This problem demonstrates key concepts in probability and statistics, including standard deviation, normal distribution, and Z-scores, applied to real-world salary scenarios.

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