In 2015, the U.S. Census Bureau reported that the median income for American households was $52,353, whereas the mean income was $71,932 (www.census.gov, data retrieved March 26, 2017). Suppose income can be represented by a lognormal variable, Y = eX, where X is normally distributed. The mean and the standard deviation of X are 11.1 and 0.4, respectively. 

a. What is the probability that a household’s income is less than $50,000?

b. What is the probability that a household’s income is greater than $60,000?

c. What is the lowest income that places a household in the 99th percentile?

d. What is the highest income that places a household in the 10th percentile?