Q6. The question is about the 2021 Pirelli C5 "hypersoft" tire that is used in F1 racing (https://www.pirelli.com/tires/en-us/motorsport/f1/tires). The engineers at team Red Bull have determined that the tire life in kiometers follows a lognormal distribution. Note that a lognormal random variable Y is, in fact, = , where X is a normally distributed random variable.Supposed the engineers suggest that the mean and the standard deviation of C5 tire life (that is, Y) are 100 kilometers and 40 kilometers, respectively. As a newly promoted race manager, you would like to know the following:

1. What are the mean and the standard deviation of the underneath X random variable?

2. What chance that a C5 tire lasts for more than 25 laps on the Dubai Autodrome race track (which is approximately 140 kilometers)?

3. What is the possibility that a C5 tire lasts for more than 40 laps on the dubai Autodrome race track (about 210 kilometers)?

4. To be safe, you want to know how many kilometers that a C5 tire could last 85% of the time. That is, you need to determine the 85th percentile of life expectancy of C5. Describe your approach in detail.