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The problem in the image asks to determine a travel time \( x \) such that 29.46% of Abby's 60 travel times exceed \( x \), assuming her travel times are normally distributed with a mean of 35.6 minutes and a standard deviation of 10.3 minutes.

### Problem Breakdown:
- Mean \( \mu = 35.6 \)
- Standard deviation \( \sigma = 10.3 \)
- We are asked to find \( x \) such that 29.46% of the values are above \( x \). This means that 70.54% of the values are below \( x \).

### Step-by-Step Solution:
1. **Find the z-score that corresponds to 70.54%**:
   Using a standard normal distribution table or calculator, we find the z-score corresponding to a cumulative probability of 0.7054.

2. **Convert the z-score to the corresponding value \( x \)** using the formula:
   \[
   x = \mu + z \sigma
   \]

Let me calculate this for you.The value of \( x \), such that 29.46% of Abby's travel times are greater than \( x \), is approximately 41.16 minutes when rounded to two decimal places.

Would you like further details or have any other questions?

Here are 5 related questions to explore further:
1. How do we interpret z-scores in the context of normal distributions?
2. What is the probability that Abby's travel time is less than 30 minutes?
3. How does changing the standard deviation affect the value of \( x \)?
4. What percentage of travel times fall between the mean and 45 minutes?
5. How would the calculation change if the travel times were not normally distributed?

**Tip:** When dealing with normal distributions, always check the cumulative probability corresponding to z-scores carefully for accurate results!

Suppose Abby tracks her travel time to work for 60 days and determines that her mean travel time, in minutes, is 35.6. Assume the travel times are normally distributed with a standard deviation of 10.3 min. Determine the travel time x such that 29.46% of the 60 days have a travel time that is greater than x. Give your answer rounded to two decimal places.

Learn how to determine the travel time x such that 29.46% of travel times are greater than x, given a mean of 35.6 minutes and a standard deviation of 10.3 minutes. This example involves the use of normal distribution, z-scores, and probability concepts. Suitable for high school students in Grades 10-12.

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