Question

Flight times for a certain airline are normally distributed with a mean of 3.25 hours and a standard deviation of 0.15 hours. Approximately what percentage of the flights last between 2.95 and 3.55 hours?

a) 68%
b) 95%
c) 99.7%
d) 50%

Answer 1

To find the percentage of flights that last between 2.95 and 3.55 hours, you can use the standard normal distribution table (z-table) to find the corresponding z-scores for these values and then find the area between these z-scores using the z-table.

Step-by-step explanation:

To find the percentage of flights that last between 2.95 and 3.55 hours, we need to find the area under the normal distribution curve between these two values. We can use the standard normal distribution table, also known as the z-table, to find the corresponding z-scores for these values. The z-score for 2.95 hours can be found by subtracting the mean (3.25 hours) and dividing by the standard deviation (0.15 hours). Similarly, the z-score for 3.55 hours can be found in the same way. Once we have the z-scores, we can use the z-table to find the percentage of flights within this range.

1. Calculate the z-score for 2.95 hours:
   z = (2.95 - 3.25) / 0.15
2. Calculate the z-score for 3.55 hours:
   z = (3.55 - 3.25) / 0.15
3. Use the z-table to find the area between these two z-scores.

By following these steps, you can determine the percentage of flights that last between 2.95 and 3.55 hours.