According to the Organisation for Economic Co operation and Development (OECD), South Koreans worked an average of 2,090 hours per year in 2011 (compared with 1,787 for workers in the United States). Assume this random variable follows a normal distribution with a standard deviation of 420 hours.

a. What is the probability that a randomly selected South Korean worked

1. Less than 1,800 hours?

2. Between 2,000 and 2,200 hours?

3. Between 1,200 and 1,600 hours?

4. Between 2,300 and 2,500 hours?

b. Confirm the answers to part a using Excel or PHStat.

c. How many hours will a South Korean work if he or she is in the 90th percentile in terms of the hours an average Korean works?