Franklin Joiner director of health education and welfare had

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 the state\'s 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 the incomes in the state could be approximated by a normal distribution and the mean per capita income was about $33,000 with a standard deviation of nearly $9,000.

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. Hint: this requires calculating two values.

Thank you!!

Solution

Z value for bottom 10% =-1.282

The required value = mean -1.282*sd = 33000-1.282*9000 = 21462

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

Z value for middle 95% = (-1.96 , 1.96)

Lower limit value = 33000-1.96*9000 =15360

Upper limit value = 33000+1.96*9000 =50640

The two values are 15360 and 50640