The Bahamas is a tropical paradise made up of 700 islands sprinkled over 100,000 square miles of the Atlantic Ocean. According to the figures released by the government of the Bahamas, the mean...

The Bahamas is a tropical paradise made up of 700 islands sprinkled over 100,000 square miles of the Atlantic Ocean. According to the figures released by the government of the Bahamas, the mean household income in the Bahamas is $36,807 and the median income is $34,270. A demographer decides to use the lognormal random variable to model this nonsymmetric income distribution. Let
Y
represent household income, where for a normally distributed
X,
Y
=
e^X
. In addition, suppose the standard deviation of household income is $12,000. Use this information to answer the following questions.

a.
Compute the mean and the standard deviation of
X.

b.
What proportion of the people in the Bahamas have household income above the mean?

c.
What proportion of the people in the Bahamas have household income below $16,000?

d.
Compute the 70th percentile of the income distribution in the Bahamas.