Each year, large sums of money are donated and collected for numerous philanthropic organizations. Since 2000, charitable donations in the United States have more than tripled to well over $250 billion. In many countries, philanthropy has been included in government policy in the form of tax exemptions for donations to these types of organizations. Today, the focus of most organizations is to the long-term goal of eliminating future need. Suppose several high schools in a city are sponsoring a walk-athon to raise money for a local charity. A certain route is mapped out through the city and each participant finds sponsors to donate money for the walk. If a participant completes the walk under a certain time, extra money will be donated. You are responsible for recording the finishing times for each of the participants. After collecting all of the data, you determine that the finishing times are normally distributed with a mean of 2.6 hours and a standard deviation of 0.3 hour.

Answer the following questions in complete sentences.

1. What percent of the players finished the walk in less than 2 hours? Show your work.

2. What is the probability that two randomly chosen players completed the walk in 2.9 hours or more? Show your work.

3. What is the probability that four randomly chosen players completed the walk between 1.7 and 2.9 hours? Show your work.

4. What observations can you make about the number of participants who complete the walk in more than 3.5 hours, given that there are 1,200 participants?

5. What might you observe if the number of participants increased or decreased?