Question

Question 2 Based on data from the 1980Census the average age of a Na'alehu County, Hawaii resident is 39 years with a standard deviation of 22. 6 . The data is normally distributed. If 100 residents are surveyed, Determine the Inter Quartile range (IQR) for the average age of the residents of this County. Please explain how you derived your answer:

Question 3 If the number of degrees of freedom for a chi-square distribution is 32. Determine the population mean and standard deviation. Please explain how you derived the answer

Answer 1

Q2) Using central limiting theorem we define the standard random variable Z as $Z={\bar{X} - 39\over 22.6/\sqrt {100}}={\bar{X} - 39\over 2.26}$

To find the IQR we have to find $Q_1,Q_3$

Now

$P(\bar X\leq Q_1) =0.25 \\ \Rightarrow P\left (Z\leq {Q_1-39\over 2.26}\right) =0.25\\ \Rightarrow {Q_1-39\over 2.26}=-0.6745~~~~~~~~~\text {Normal table} \\ \Rightarrow Q_1=37.4756$ $P(\bar X\geq Q_3) =0.25 \\ \Rightarrow P\left (Z\geq {Q_3-39\over 2.26}\right) =0.25\\ \Rightarrow {Q_3-39\over 2.26}=0.6745~~~~~~~~~\text {Normal table} \\ \Rightarrow Q_3= 40.5244$

Hence $\hfox{\text {IQR } = 40.5244-37.4756=3.0488}$