An advertising company plans to market a product to lowincom

An advertising company plans to market a product to low-income families. A study states that for a particular area, the average income per family is $24,596 and the standard deviation is $6,256. If the company plans to target the bottom 18% of the families based on income, find the cutoff income. Assume the variable is normally distributed.

Solution

Given X~Normal(mean=24596, s=6256) P(X P((X-mean)/s <(c-24596)/6256)=0.18 --> P(Z<(c-24596)/6256)=0.18 --> (c-24596)/6256= -0.92 (check standard normal table) --> c=24596-0.92*6256=18840.48