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Hello!
Can someone help me understand how to go about answering these questions for binomial distributions? 

 

n=8, p=0.2

Find P(X=3)

Find P(X≤3) 

Find P(X>4)

Find P(X<5)

Find P(X≥3)

Find P(3

 

I know these are alot of questions but I missed this lesson because of an illness and have a test to write tomorrow and have zero information on how to answer/do them. 

Any help would be very much appreciated! Thank you! 

saarad0  Oct 29, 2017
 #1
avatar+86931 
+3

Not an expert on these....but I believe that we have :

 

8  = number of trials    p = probability of success on any trial = .2    

  probability of failure on one trial  = 1 - .2  = .8

 

P(3)  = means "probability of  3 successes in 8  trials "  =

  C(8,3) (.2)^3 (1 - .2)^(8-3)  = C(8,3) (.2)^3 (.8)^5  ≈  14.68%

 

 P (≤3 ) = means probability of  0 successes in 8 trials + probability of  1 success in 8  trials + probability of  2 successes in 8  trials + probability of  3 success in 8  trials  = 

C (8,0) (.2)^0 (.8)^8  +  C (8,1) (.2)^1 (.8)^7 + C (8,2) (.2)^2 (.8)^6 + C (8,3) (.2)^3 (.8)^5  ≈

94.37%

 

P ( > 4) = 

C (8,5) (.2)^5 (.8)^3  +  C (8,6) (.2)^6 (.8)^2 + C (8,7) (.2)^7 (.8)^1 + C (8,8) (.2)^8 (.8)^0  ≈

1.04%

 

Based on this....Can you do the rest ???...if not....let me know....

 

Here's some more info :  http://www.mathwords.com/b/binomial_probability_formula.htm

 

Note also  :  P(> 4)  = 1 - P( ≤ 4 )

 

 

cool cool cool

CPhill  Oct 29, 2017
 #2
avatar+27 
+3

Yes! This helped loads! I seem to get it now. 

Thank you for your time!

 

:) 

saarad0  Oct 29, 2017

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