Question

A political consultant is developing a contact list for his client. The client will use the list to target the youngest 19 percent of registered voters in the district. The age of registered voters is normally distributed with a mean of 51 and a standard deviation of 14. What is the age of the oldest person targeted by this contact list? (Round your value to the nearest whole number).

Answer 1

$X \sim N ( \mu = 51 , \sigma = 14 )$

$Z = ( X - \mu ) / \sigma$

P ( Z < ? ) = 19% = 0.19

Looking for the probability of 0.19 in standard normal tabel to find the critical value Z

Z = - 0.88

X = 38.68 $\approx$ 39

X = 39