Question

Economists frequently make use of quintiles (i.e., the 20th, 40th, 60th, and 80th percentiles) particularly

when discussing incomes. Suppose that in a large city household incomes are normally distributed

with a mean of $50,000 and a standard deviation of $10,000. An economist wishes to identify the

quintiles. Unfortunately, he did not pass his statistics course. Help him by providing the quintiles.

Answer 1

Given :

mean= 50000; sd= 10000

To find 20th percentile, that is $p(Z_a)=0.2$

Using ti84, invnorm(0.2)= -0.842.Hence Z= -0.842.

therefore using Z score formula, $x=Z*sd+mean$

$x= -0.842*10000+50000=41580$

To find 40th percentile, that is $p(Z_a)=0.4$

Using ti84, invnorm(0.4)= -0.253.Hence Z= -0.253.

therefore using Z score formula,$x=Z*sd+mean\\$

$x= -0.253*10000+50000=47470$

To find 40th percentile, that is $p(Z_a)=0.6$

Using ti84, invnorm(0.6)= 0.253.Hence Z= 0.253.

therefore using Z score formula,$x=Z*sd+mean\\$

$x=0.253*10000+50000$ =52530

To find 40th percentile, that is $p(Z_a)=0.8$

Using ti84, invnorm(0.8)=0.842.Hence Z= 0.842.

therefore using Z score formula,$x=Z*sd+mean\\$

$x= 0.842*10000+50000=58420$