SOLUTION: Eighty percent of the applications received for a particular position are accepted. For the next fourteen applications, calculate: (round the answer to 4 decimal places if neede

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Question 1119336: Eighty percent of the applications received for a particular position are accepted. For the next fourteen applications, calculate:
(round the answer to 4 decimal places if needed!)
a) What is the probability that less than 2 applications will be rejected?
b) What is the probability that none of the applications will be rejected?
c) What is the probability that all of the applications will be rejected?
d) What is the probability that at least 2 applications will be accepted?
e) Determine the variance of the rejected applications.?
Answer by ikleyn(52795) About Me  (Show Source):
You can put this solution on YOUR website!
.

You are given that the probability for an application to be accepted is  0.8;  the probability to be rejected is  0.2.


(a)  What is the probability that less than 2 applications will be rejected? 

     = the probability that 0 apps will be rejected or 1 (one) of 14 apps will be rejected =

     = 0.8%5E14 + C%5B14%5D%5E1%2A0.8%5E13%2A0.2 = 0.2%5E14 + 14%2A0.8%5E13%2A0.2.


     Calculate it on your own.


(b)  What is the probability that none of the applications will be rejected? 

    = the probability that all of 14 apps will be accepted = 

    = 0.8%5E14.


     Calculate it on your own.


(c)  What is the probability that all of the applications will be rejected? 

     0.2%5E14.


     Calculate it on your own.


d)  What is the probability that at least 2 applications will be accepted? 

     = the COMPLEMENT to the probability that 14 of 14, or 13 of 14 will be rejected =

     = 1 - (0.2%5E14 + C%5B14%5D%5E1%2A0.2%5E13%2A0.8) = 1 - (0.2%5E14 + 14%2A0.2%5E13%2A0.8).


     Calculate it on your own.


I answered questions   (a) - (d).