Question 323536
Approximately 53% of all the US population have at least some college education. Choose 10 people at random. Find the probabilities.
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Binomial problem with n=10 ; p = 0.53
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A.Exactly 1/2 have some college education
P(x=5) = 10C5*(0.53)^5(0.47)^5 = 0.2417
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B.At least 1 has some college education
P(x>=1) = 1 - P(x = 0) 
= 1 - 10C0(0.53)^0*0.47^10 
= 1 - 0.47^10 
= 0.9997
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C.Fewer than 5 have some college education
I used a TI-84 to get:
P(0<= x <=4) = binomcdf(10,0,53,4) = 0.3057
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D. What is the most likely number of people that have some college education?
mean = E(x) = np = 10*0.53 = 5.3 people
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Cheers,
Stan H.



 
For parts A and B I used the factorial equation: P(x)= n!/x!(n-x)! *p^x(1-p)^n-x 
For A I got: .242
For B I got: .006