1) Companies which design furniture for elementary school classrooms create a variety of sizes for kids of various ages.  Assume the heights of kindergarten children can be describeed by a Normal distribution with a mean of 37.2 inches and standard deviation of 2.1 inches.

a) What fraction of kids must the company expect to be less than 35 inches tall?

b) In what height interval must the company expect to determine the middle 70% of kindergarteners?

c) At least how tall are the biggest 15% of students?

2) Bank Accounts: You work for business analytics department of a large commercial bank, and you learn that balances of small-business accounts are distributed on log-scale according to a normal distribution.  You also learn that the lower and upper quartiles of the balances are $500 and $50,000, respectively.  In the sub-problems given below you will end up inferring in small steps what a 95% range of the bank balances is.

a) Determine the lower and upper quartiles of the log10-balances?

b) Determine the mean and standard deviation of log10-balances?

c) Determine a 95% range of the log10-balances?

d) Determine a 95% range of the balances in $s?  Express in English what the two boundaries mean.