Franklin Joiner, director of health, education, and welfare, had just left a meeting with the state’s newly elected governor and several of the other recently appointed department heads. One of the governor’s campaign promises was to try to halt the rising cost of a certain state entitlement program. In several speeches, the governor indicated the state of Idaho should allocate funds only to those individuals ranked in the bottom 10% of the state’s income distribution. Now the governor wants to know how much one could earn before being disqualified from the program, and he also wants to know the range of incomes for the middle 95% of the state’s income distribution. Frank had mentioned in the meeting that he thought incomes in the state could be approximated by a normal distribution and that mean per capita income was about $33,000 with a standard deviation of nearly $9,000. The governor was expecting a memo in his office by 3:00 p.m. that afternoon with answers to his questions.

Required Tasks:

1. Assuming that incomes can be approximated using a normal distribution with the specified mean and standard deviation, calculate the income that cut off the bottom 10% of incomes.

2. Assuming that incomes can be approximated using a normal distribution with the specified mean and standard deviation, calculate the middle 95% of incomes. This requires calculating two values. 

3. Write a short memo describing your results and how they were obtained. Your memo should clearly state the income that would disqualify people from the program, as well as the range of incomes in the middle 95% of the state’s income distribution.