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?

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.