A recruiting firm finds that 20% of the applicants for a particular sales positi
ID: 3023557 • Letter: A
Question
A recruiting firm finds that 20% of the applicants for a particular sales position are fluent in both English and Spanish. Applicants are selected at random from the pool and interviewed sequentially. Suppose that the first applicant who is fluent in both English and Spanish is offered the position, and the applicant accepts. Suppose each interview costs $125. The expected value and standard deviation of the cost of interviewing until the job is filled. are, respectively,
a. $2034.15 and $20.
b. $250 and $131.1
c. $625 and $559.017
d. $500 and $100.921
e. $1000.45 and $125.18
Explanation / Answer
since the probability is until the job is filled the distribution of this probability is geometric so
mean = 1 / p * cost
SD = srqt ( q / p^2 ) * cost
cost = $125
p = 0.20
q = 1-p = 1 - 0.20 = 0.80
expected value will be = 1/0.20 * 125 = 625
SD = srqt ( 0.80 / 0.20^2 ) * 125 = 559.017