Final answer:
To find the travel time that has 26.11% of the days being longer, we use the z-score for the 73.89% cumulative probability and the formula for converting a z-score to an original value, which results in approximately 41.99 minutes.
Step-by-step explanation:
The student is asking to find a specific travel time that divides the upper 26.11% of her travel times from the lower 73.89%, given that the mean travel time is 35.6 minutes and the standard deviation is 10.3 minutes with a normal distribution. This value corresponds to a certain z-score. First, we find the z-score that corresponds to the cumulative probability of 73.89% (which is 1 - 26.11%). Using a z-table or a calculator, we find that the z-score for 73.89% is approximately 0.62. Next, we use the formula for converting a z-score to the original value, which is X = μ + (z * σ), where μ is the mean, σ is the standard deviation, and z is the z-score. Substituting the given values, we calculate X as follows: X = 35.6 + (0.62 * 10.3) ≈ 35.6 + 6.386 ≈ 41.986. Therefore, the travel time such that 26.11% of the 60 days have a travel time that is longer is approximately 41.99 minutes when rounded to two decimal places.