SOLUTION: Question 1 A telemarketing company that sells homeowner insurance has found that 15% of all calls made to households lead to a sale of a homeowner insurance policy. Assume that

Algebra ->  Probability-and-statistics -> SOLUTION: Question 1 A telemarketing company that sells homeowner insurance has found that 15% of all calls made to households lead to a sale of a homeowner insurance policy. Assume that       Log On


   

Question 1178413: Question 1
A telemarketing company that sells homeowner insurance has found that 15% of
all calls made to households lead to a sale of a homeowner insurance policy.
Assume that each call is independent of all other calls.
(a) Find the probability that no sales result from 12 calls.
(b) What is the likelihood that fewer than three homeowner policies are sold in
15 calls?
Answer by ikleyn(53937) About Me  (Show Source):
You can put this solution on YOUR website!
Question 1
A telemarketing company that sells homeowner insurance has found that 15% of
all calls made to households lead to a sale of a homeowner insurance policy.
Assume that each call is independent of all other calls.
(a) Find the probability that no sales result from 12 calls.
(b) What is the likelihood that fewer than three homeowner policies are sold in
15 calls?
~~~~~~~~~~~~~~~~~ 


(a)  P = %281-0.15%29%5E12 = 0.85%5E12 = 0.142242 = 14.22%.      ANSWER


(b)  It is a binomial distribution probability problem.

        - number of trials        n =  15;
        - number of success trial k <   3;
        - Probability of success on a single trial p = 0.15.



We need calculate  P(n=15; k < 3; p=0.15).      


To facilitate calculations, I use an appropriate online (free of charge) calculator at this web-site 

https://stattrek.com/online-calculator/binomial.aspx


It provides nice instructions  and  a convenient input and output for all relevant options/cases.


    P(n=15; k < 3; p=0.15) = 0.6042,   or  60/42% (rounded).       ANSWER

Solved.

---------------

To see a variety similar solved problems,  look into the lessons
    - Simple and simplest probability problems on Binomial distribution
    - Typical binomial distribution probability problems
    - How to calculate Binomial probabilities with Technology (using MS Excel)
    - Solving problems on Binomial distribution with Technology (using MS Excel)
    - Solving problems on Binomial distribution with Technology (using online solver)
in this site.

After reading these lessons,  you will be able to solve such problems on your own,
which is your  PRIMARY  MAJOR  GOAL  visiting this forum  (I believe).