Bank Accounts: You work for business analytics department of large commercial bank, and you learn that the balances of the small-business accounts are distributed on log-scale according to normal distribution. You also learn that the lower and upper quartiles of balances are $500 and $50,000, respectively. In following sub-problems you will end up inferring in small steps what a 95% range of the bank balances is. (For ease of grading, employ the memorized rounded multipliers for normal quantiles, not the more exact values from the tables or calculators.)
a) What are the lower and upper quartiles of log10-balances?
b) What are the mean and sd of log10-balances?
c) What is a 95% range of log10-balances?
d) What is a 95% range of the balances in $s? Express in English what the two boundaries mean.