To find the z-scores for the given vacation expense amounts, we can use the z-score formula:

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

Where:

• $x$ is the value for which we are finding the z-score,
• $\mu = 247$ is the mean (average expense per day),
• $\sigma = 60$ is the standard deviation.

Let's calculate the z-scores for each of the given values:

a. For $x = 197$:

$z = \frac{197 - 247}{60} = \frac{-50}{60} = -0.83$ The z-score for $197 per day is -0.83.

b. For $x = 277$:

$z = \frac{277 - 247}{60} = \frac{30}{60} = 0.50$ The z-score for $277 per day is 0.50.

c. For $x = 310$:

$z = \frac{310 - 247}{60} = \frac{63}{60} = 1.05$ The z-score for $310 per day is 1.05.

Summary:

• a. $197 per day: $z = -0.83$
• b. $277 per day: $z = 0.50$
• c. $310 per day: $z = 1.05$

Would you like further details or have any questions about these calculations?

Here are 5 related questions you could explore:

1. What does a z-score of 0 represent in a normal distribution?
2. How can we interpret negative z-scores in real-life scenarios?
3. What is the probability of spending less than $197 per day?
4. How would the z-scores change if the standard deviation was larger or smaller?
5. How can we use z-scores to determine outliers in this data?

Tip: A z-score tells you how many standard deviations a data point is from the mean. It helps standardize different scales or data sets for comparison.